TSTP Solution File: GRP194+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n006.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 : 600s
% DateTime : Sat Jul 16 09:01:14 EDT 2022
% Result : Theorem 0.24s 1.42s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 10 unt; 0 def)
% Number of atoms : 82 ( 14 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 84 ( 36 ~; 34 |; 8 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 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 : 46 ( 3 sgn 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_zero,axiom,
! [X1,X2] :
( left_zero(X1,X2)
<=> ( group_member(X2,X1)
& ! [X3] :
( group_member(X3,X1)
=> multiply(X1,X2,X3) = X2 ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',left_zero) ).
fof(homomorphism1,axiom,
! [X2] :
( group_member(X2,f)
=> group_member(phi(X2),h) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',homomorphism1) ).
fof(homomorphism2,axiom,
! [X2,X3] :
( ( group_member(X2,f)
& group_member(X3,f) )
=> multiply(h,phi(X2),phi(X3)) = phi(multiply(f,X2,X3)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',homomorphism2) ).
fof(total_function,axiom,
! [X1,X2,X3] :
( ( group_member(X2,X1)
& group_member(X3,X1) )
=> group_member(multiply(X1,X2,X3),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP007+0.ax',total_function) ).
fof(left_zero_for_f,hypothesis,
left_zero(f,f_left_zero),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',left_zero_for_f) ).
fof(surjective,axiom,
! [X2] :
( group_member(X2,h)
=> ? [X3] :
( group_member(X3,f)
& phi(X3) = X2 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',surjective) ).
fof(prove_left_zero_h,conjecture,
left_zero(h,phi(f_left_zero)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_left_zero_h) ).
fof(c_0_7,plain,
! [X4,X5,X6,X4,X5] :
( ( group_member(X5,X4)
| ~ left_zero(X4,X5) )
& ( ~ group_member(X6,X4)
| multiply(X4,X5,X6) = X5
| ~ left_zero(X4,X5) )
& ( group_member(esk1_2(X4,X5),X4)
| ~ group_member(X5,X4)
| left_zero(X4,X5) )
& ( multiply(X4,X5,esk1_2(X4,X5)) != X5
| ~ group_member(X5,X4)
| left_zero(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[left_zero])])])])])])]) ).
fof(c_0_8,plain,
! [X3] :
( ~ group_member(X3,f)
| group_member(phi(X3),h) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[homomorphism1])]) ).
fof(c_0_9,plain,
! [X4,X5] :
( ~ group_member(X4,f)
| ~ group_member(X5,f)
| multiply(h,phi(X4),phi(X5)) = phi(multiply(f,X4,X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[homomorphism2])]) ).
fof(c_0_10,plain,
! [X4,X5,X6] :
( ~ group_member(X5,X4)
| ~ group_member(X6,X4)
| group_member(multiply(X4,X5,X6),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[total_function])]) ).
cnf(c_0_11,plain,
( multiply(X1,X2,X3) = X2
| ~ left_zero(X1,X2)
| ~ group_member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,hypothesis,
left_zero(f,f_left_zero),
inference(split_conjunct,[status(thm)],[left_zero_for_f]) ).
cnf(c_0_13,plain,
( group_member(X2,X1)
| ~ left_zero(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( group_member(phi(X1),h)
| ~ group_member(X1,f) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( multiply(h,phi(X1),phi(X2)) = phi(multiply(f,X1,X2))
| ~ group_member(X2,f)
| ~ group_member(X1,f) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( group_member(multiply(X1,X2,X3),X1)
| ~ group_member(X3,X1)
| ~ group_member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,hypothesis,
( multiply(f,f_left_zero,X1) = f_left_zero
| ~ group_member(X1,f) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,hypothesis,
group_member(f_left_zero,f),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
fof(c_0_19,plain,
! [X4] :
( ( group_member(esk2_1(X4),f)
| ~ group_member(X4,h) )
& ( phi(esk2_1(X4)) = X4
| ~ group_member(X4,h) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[surjective])])])])])]) ).
cnf(c_0_20,plain,
( group_member(multiply(h,phi(X1),phi(X2)),h)
| ~ group_member(X2,f)
| ~ group_member(X1,f) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_21,hypothesis,
( multiply(h,phi(f_left_zero),phi(X1)) = phi(f_left_zero)
| ~ group_member(X1,f) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_17]),c_0_18])]) ).
fof(c_0_22,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(assume_negation,[status(cth)],[prove_left_zero_h]) ).
cnf(c_0_23,plain,
( phi(esk2_1(X1)) = X1
| ~ group_member(X1,h) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( group_member(esk2_1(X1),f)
| ~ group_member(X1,h) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,hypothesis,
( group_member(phi(f_left_zero),h)
| ~ group_member(X1,f) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_18])]) ).
fof(c_0_26,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( left_zero(X1,X2)
| ~ group_member(X2,X1)
| multiply(X1,X2,esk1_2(X1,X2)) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_28,hypothesis,
( multiply(h,phi(f_left_zero),X1) = phi(f_left_zero)
| ~ group_member(X1,h) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_23]),c_0_24]) ).
cnf(c_0_29,hypothesis,
group_member(phi(f_left_zero),h),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_30,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,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_27,c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_32,plain,
( left_zero(X1,X2)
| group_member(esk1_2(X1,X2),X1)
| ~ group_member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_33,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_29])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 12:07:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.24/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.42 # Preprocessing time : 0.014 s
% 0.24/1.42
% 0.24/1.42 # Proof found!
% 0.24/1.42 # SZS status Theorem
% 0.24/1.42 # SZS output start CNFRefutation
% See solution above
% 0.24/1.42 # Proof object total steps : 34
% 0.24/1.42 # Proof object clause steps : 20
% 0.24/1.42 # Proof object formula steps : 14
% 0.24/1.42 # Proof object conjectures : 4
% 0.24/1.42 # Proof object clause conjectures : 1
% 0.24/1.42 # Proof object formula conjectures : 3
% 0.24/1.42 # Proof object initial clauses used : 11
% 0.24/1.42 # Proof object initial formulas used : 7
% 0.24/1.42 # Proof object generating inferences : 9
% 0.24/1.42 # Proof object simplifying inferences : 12
% 0.24/1.42 # Training examples: 0 positive, 0 negative
% 0.24/1.42 # Parsed axioms : 8
% 0.24/1.42 # Removed by relevancy pruning/SinE : 0
% 0.24/1.42 # Initial clauses : 12
% 0.24/1.42 # Removed in clause preprocessing : 0
% 0.24/1.42 # Initial clauses in saturation : 12
% 0.24/1.42 # Processed clauses : 41
% 0.24/1.42 # ...of these trivial : 0
% 0.24/1.42 # ...subsumed : 4
% 0.24/1.42 # ...remaining for further processing : 37
% 0.24/1.42 # Other redundant clauses eliminated : 0
% 0.24/1.42 # Clauses deleted for lack of memory : 0
% 0.24/1.42 # Backward-subsumed : 2
% 0.24/1.42 # Backward-rewritten : 3
% 0.24/1.42 # Generated clauses : 160
% 0.24/1.42 # ...of the previous two non-trivial : 120
% 0.24/1.42 # Contextual simplify-reflections : 9
% 0.24/1.42 # Paramodulations : 160
% 0.24/1.42 # Factorizations : 0
% 0.24/1.42 # Equation resolutions : 0
% 0.24/1.42 # Current number of processed clauses : 32
% 0.24/1.42 # Positive orientable unit clauses : 5
% 0.24/1.42 # Positive unorientable unit clauses: 0
% 0.24/1.42 # Negative unit clauses : 2
% 0.24/1.42 # Non-unit-clauses : 25
% 0.24/1.42 # Current number of unprocessed clauses: 53
% 0.24/1.42 # ...number of literals in the above : 239
% 0.24/1.42 # Current number of archived formulas : 0
% 0.24/1.42 # Current number of archived clauses : 5
% 0.24/1.42 # Clause-clause subsumption calls (NU) : 98
% 0.24/1.42 # Rec. Clause-clause subsumption calls : 89
% 0.24/1.42 # Non-unit clause-clause subsumptions : 15
% 0.24/1.42 # Unit Clause-clause subsumption calls : 0
% 0.24/1.42 # Rewrite failures with RHS unbound : 0
% 0.24/1.42 # BW rewrite match attempts : 6
% 0.24/1.42 # BW rewrite match successes : 2
% 0.24/1.42 # Condensation attempts : 0
% 0.24/1.42 # Condensation successes : 0
% 0.24/1.42 # Termbank termtop insertions : 3802
% 0.24/1.42
% 0.24/1.42 # -------------------------------------------------
% 0.24/1.42 # User time : 0.014 s
% 0.24/1.42 # System time : 0.005 s
% 0.24/1.42 # Total time : 0.019 s
% 0.24/1.42 # Maximum resident set size: 2808 pages
%------------------------------------------------------------------------------