%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP194+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:38:57 PM UTC 2026
% Result : Theorem 0.16s 0.58s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 11 unt; 0 def)
% Number of atoms : 84 ( 14 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 87 ( 38 ~; 35 |; 8 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 47 ( 1 sgn 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(total_function,axiom,
! [X1,X2,X3] :
( ( group_member(X3,X1)
& group_member(X2,X1) )
=> group_member(multiply(X1,X2,X3),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP007+0.ax',total_function) ).
fof(homomorphism2,axiom,
! [X2,X3] :
( ( group_member(X3,f)
& group_member(X2,f) )
=> multiply(h,phi(X2),phi(X3)) = phi(multiply(f,X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
fof(homomorphism1,axiom,
! [X2] :
( group_member(X2,f)
=> group_member(phi(X2),h) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
fof(left_zero,axiom,
! [X1,X2] :
( left_zero(X1,X2)
<=> ( ! [X3] :
( group_member(X3,X1)
=> multiply(X1,X2,X3) = X2 )
& group_member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero) ).
fof(surjective,axiom,
! [X2] :
( group_member(X2,h)
=> ? [X3] :
( phi(X3) = X2
& group_member(X3,f) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
fof(left_zero_for_f,hypothesis,
left_zero(f,f_left_zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero_for_f) ).
fof(prove_left_zero_h,conjecture,
left_zero(h,phi(f_left_zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_zero_h) ).
fof(c_0_7,plain,
! [X16,X17,X18] :
( group_member(multiply(X16,X17,X18),X16)
| ~ group_member(X18,X16)
| ~ group_member(X17,X16) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[total_function])])]) ).
fof(c_0_8,plain,
! [X12,X13] :
( multiply(h,phi(X12),phi(X13)) = phi(multiply(f,X12,X13))
| ~ group_member(X13,f)
| ~ group_member(X12,f) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[homomorphism2])])]) ).
fof(c_0_9,plain,
! [X11] :
( group_member(phi(X11),h)
| ~ group_member(X11,f) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[homomorphism1])])]) ).
fof(c_0_10,plain,
! [X5,X6,X7,X8,X9] :
( ( left_zero(X8,X9)
| ~ group_member(X9,X8)
| multiply(X8,X9,esk1_2(X8,X9)) != X9 )
& ( left_zero(X8,X9)
| ~ group_member(X9,X8)
| group_member(esk1_2(X8,X9),X8) )
& ( ~ left_zero(X5,X6)
| multiply(X5,X6,X7) = X6
| ~ group_member(X7,X5) )
& ( ~ left_zero(X5,X6)
| group_member(X6,X5) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[left_zero])])])])])])]) ).
fof(c_0_11,plain,
! [X14] :
( ( ~ group_member(X14,h)
| phi(esk2_1(X14)) = X14 )
& ( ~ group_member(X14,h)
| group_member(esk2_1(X14),f) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[surjective])])])])]) ).
cnf(c_0_12,plain,
( ~ group_member(X3,X2)
| ~ group_member(X1,X2)
| group_member(multiply(X2,X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( ~ group_member(X2,f)
| ~ group_member(X1,f)
| multiply(h,phi(X1),phi(X2)) = phi(multiply(f,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ group_member(X1,f)
| group_member(phi(X1),h) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ left_zero(X2,X3)
| ~ group_member(X1,X2)
| multiply(X2,X3,X1) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
left_zero(f,f_left_zero),
inference(split_conjunct,[status(thm)],[left_zero_for_f]) ).
cnf(c_0_17,plain,
( ~ left_zero(X2,X1)
| group_member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_18,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(assume_negation,[status(cth)],[prove_left_zero_h]) ).
cnf(c_0_19,plain,
( ~ group_member(X1,h)
| phi(esk2_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
( ~ group_member(X1,h)
| group_member(esk2_1(X1),f) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,plain,
( ~ group_member(X1,f)
| ~ group_member(X2,f)
| group_member(phi(multiply(f,X1,X2)),h) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_14]) ).
cnf(c_0_22,hypothesis,
( ~ group_member(X1,f)
| multiply(f,f_left_zero,X1) = f_left_zero ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,hypothesis,
group_member(f_left_zero,f),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
fof(c_0_24,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( ~ group_member(X2,h)
| ~ group_member(X1,f)
| phi(multiply(f,X1,esk2_1(X2))) = multiply(h,phi(X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_19]),c_0_20]) ).
cnf(c_0_26,hypothesis,
( ~ group_member(X1,f)
| group_member(phi(f_left_zero),h) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
fof(c_0_27,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(fof_nnf,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
( ~ group_member(X2,X1)
| multiply(X1,X2,esk1_2(X1,X2)) != X2
| left_zero(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_29,hypothesis,
( ~ group_member(X1,h)
| multiply(h,phi(f_left_zero),X1) = phi(f_left_zero) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_23])]),c_0_20]) ).
cnf(c_0_30,hypothesis,
group_member(phi(f_left_zero),h),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_31,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,hypothesis,
~ group_member(esk1_2(h,phi(f_left_zero)),h),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_33,plain,
( ~ group_member(X2,X1)
| left_zero(X1,X2)
| group_member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_34,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_30])]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP194+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.51 % Computer : n001.cluster.edu
% 0.09/0.51 % Model : x86_64 x86_64
% 0.09/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.51 % Memory : 8046.5625MB
% 0.09/0.51 % OS : Linux 6.8.0-71-generic
% 0.09/0.51 % CPULimit : 300
% 0.09/0.51 % WCLimit : 300
% 0.09/0.51 % DateTime : Sun Sep 20 20:10:58 UTC 2026
% 0.09/0.51 % CPUTime :
% 0.09/0.51 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.55 Running first-order theorem proving
% 0.09/0.56 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.16/0.58 % Version: 3.5.1
% 0.16/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.58 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.58 % Starting sh5l with 300s (1) cores
% 0.16/0.58 % new_bool_1 with pid 1288781 completed with status 0
% 0.16/0.58 % Result found by new_bool_1
% 0.16/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.58 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.58 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.58 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.58 % Search class: FGUSF-FFSF31-SFFFFFNN
% 0.16/0.58 % partial match(1): FGUSF-FFSF32-SFFFFFNN
% 0.16/0.58 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.58 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.58 % SubtermCWHack with pid 1288783 completed with status 0
% 0.16/0.58 % Result found by SubtermCWHack
% 0.16/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.58 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.58 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.58 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.58 % Search class: FGUSF-FFSF31-SFFFFFNN
% 0.16/0.58 % partial match(1): FGUSF-FFSF32-SFFFFFNN
% 0.16/0.58 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.58 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.58 % Preprocessing time : 0.001 s
% 0.16/0.58
% 0.16/0.58 % Proof found!
% 0.16/0.58 % SZS status Theorem
% 0.16/0.58 % SZS output start CNFRefutation
% See solution above
% 0.16/0.58 % Parsed axioms : 8
% 0.16/0.58 % Removed by relevancy pruning/SinE : 0
% 0.16/0.58 % Initial clauses : 12
% 0.16/0.58 % Removed in clause preprocessing : 0
% 0.16/0.58 % Initial clauses in saturation : 12
% 0.16/0.58 % Processed clauses : 19
% 0.16/0.58 % ...of these trivial : 0
% 0.16/0.58 % ...subsumed : 0
% 0.16/0.58 % ...remaining for further processing : 19
% 0.16/0.58 % Other redundant clauses eliminated : 0
% 0.16/0.58 % Clauses deleted for lack of memory : 0
% 0.16/0.58 % Backward-subsumed : 0
% 0.16/0.58 % Backward-rewritten : 1
% 0.16/0.58 % Generated clauses : 22
% 0.16/0.58 % ...of the previous two non-redundant : 17
% 0.16/0.58 % ...aggressively subsumed : 0
% 0.16/0.58 % Contextual simplify-reflections : 4
% 0.16/0.58 % Paramodulations : 22
% 0.16/0.58 % Factorizations : 0
% 0.16/0.58 % NegExts : 0
% 0.16/0.58 % Equation resolutions : 0
% 0.16/0.58 % Disequality decompositions : 0
% 0.16/0.58 % Total rewrite steps : 12
% 0.16/0.58 % ...of those cached : 9
% 0.16/0.58 % Propositional unsat checks : 0
% 0.16/0.58 % Propositional check models : 0
% 0.16/0.58 % Propositional check unsatisfiable : 0
% 0.16/0.58 % Propositional clauses : 0
% 0.16/0.58 % Propositional clauses after purity: 0
% 0.16/0.58 % Propositional unsat core size : 0
% 0.16/0.58 % Propositional preprocessing time : 0.000
% 0.16/0.58 % Propositional encoding time : 0.000
% 0.16/0.58 % Propositional solver time : 0.000
% 0.16/0.58 % Success case prop preproc time : 0.000
% 0.16/0.58 % Success case prop encoding time : 0.000
% 0.16/0.58 % Success case prop solver time : 0.000
% 0.16/0.58 % Current number of processed clauses : 18
% 0.16/0.58 % Positive orientable unit clauses : 3
% 0.16/0.58 % Positive unorientable unit clauses: 0
% 0.16/0.58 % Negative unit clauses : 2
% 0.16/0.58 % Non-unit-clauses : 13
% 0.16/0.58 % Current number of unprocessed clauses: 7
% 0.16/0.58 % ...number of literals in the above : 29
% 0.16/0.58 % Current number of archived formulas : 0
% 0.16/0.58 % Current number of archived clauses : 1
% 0.16/0.58 % Clause-clause subsumption calls (NU) : 30
% 0.16/0.58 % Rec. Clause-clause subsumption calls : 25
% 0.16/0.58 % Non-unit clause-clause subsumptions : 4
% 0.16/0.58 % Unit Clause-clause subsumption calls : 0
% 0.16/0.58 % Rewrite failures with RHS unbound : 0
% 0.16/0.58 % BW rewrite match attempts : 1
% 0.16/0.58 % BW rewrite match successes : 1
% 0.16/0.58 % Condensation attempts : 0
% 0.16/0.58 % Condensation successes : 0
% 0.16/0.58 % Termbank termtop insertions : 1288
% 0.16/0.58 % Search garbage collected termcells : 183
% 0.16/0.58
% 0.16/0.58 % -------------------------------------------------
% 0.16/0.58 % User time : 0.004 s
% 0.16/0.58 % System time : 0.002 s
% 0.16/0.58 % Total time : 0.006 s
% 0.16/0.58 % Maximum resident set size: 3640 pages
% 0.16/0.58
% 0.16/0.58 % -------------------------------------------------
% 0.16/0.58 % User time : 0.005 s
% 0.16/0.58 % System time : 0.007 s
% 0.16/0.58 % Total time : 0.011 s
% 0.16/0.58 % Maximum resident set size: 4864 pages
% 0.16/0.58 % E exiting
%------------------------------------------------------------------------------