TSTP Solution File: HEN008-2 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : HEN008-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n023.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 17:51:01 EDT 2023
% Result : Unsatisfiable 19.79s 2.92s
% Output : CNFRefutation 19.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of clauses : 69 ( 28 unt; 0 nHn; 53 RR)
% Number of literals : 153 ( 11 equ; 86 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 153 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(divisor_existence,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',divisor_existence) ).
cnf(aQc,hypothesis,
quotient(a,c,aQc),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',aQc) ).
cnf(transitivity_of_less_equal,axiom,
( less_equal(X1,X3)
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X3) ),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',transitivity_of_less_equal) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',closure) ).
cnf(aLEb,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',aLEb) ).
cnf(x_divde_zero_is_x,axiom,
quotient(X1,zero,X1),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',x_divde_zero_is_x) ).
cnf(xQyLEz_implies_xQzLEy,axiom,
( less_equal(X5,X2)
| ~ quotient(X1,X2,X3)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X4,X5) ),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',xQyLEz_implies_xQzLEy) ).
cnf(less_equal_and_equal,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',less_equal_and_equal) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',zero_is_smallest) ).
cnf(quotient_property,axiom,
( less_equal(X7,X8)
| ~ quotient(X1,X2,X3)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X4,X6)
| ~ quotient(X6,X5,X7)
| ~ quotient(X3,X4,X8) ),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',quotient_property) ).
cnf(xLEy_implies_zQyLEzQx,axiom,
( less_equal(X4,X5)
| ~ less_equal(X1,X2)
| ~ quotient(X3,X2,X4)
| ~ quotient(X3,X1,X5) ),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',xLEy_implies_zQyLEzQx) ).
cnf(quotient_less_equal,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',quotient_less_equal) ).
cnf(well_defined,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',well_defined) ).
cnf(zero_divide_anything_is_zero,axiom,
quotient(zero,X1,zero),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',zero_divide_anything_is_zero) ).
cnf(bQc,hypothesis,
quotient(b,c,bQc),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',bQc) ).
cnf(prove_aQcLEbQc,negated_conjecture,
~ less_equal(aQc,bQc),
file('/export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p',prove_aQcLEbQc) ).
cnf(c_0_16,axiom,
( less_equal(X3,X1)
| ~ quotient(X1,X2,X3) ),
divisor_existence ).
cnf(c_0_17,hypothesis,
quotient(a,c,aQc),
aQc ).
cnf(c_0_18,axiom,
( less_equal(X1,X3)
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X3) ),
transitivity_of_less_equal ).
cnf(c_0_19,hypothesis,
less_equal(aQc,a),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,hypothesis,
( less_equal(X1,a)
| ~ less_equal(X1,aQc) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_22,hypothesis,
less_equal(a,b),
aLEb ).
cnf(c_0_23,hypothesis,
( less_equal(X1,a)
| ~ less_equal(X2,aQc)
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_24,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_25,axiom,
quotient(X1,zero,X1),
x_divde_zero_is_x ).
cnf(c_0_26,hypothesis,
( less_equal(X1,b)
| ~ less_equal(X1,a) ),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_27,hypothesis,
( less_equal(X1,a)
| ~ less_equal(X1,divide(aQc,X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
less_equal(X1,X1),
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_29,axiom,
( less_equal(X5,X2)
| ~ quotient(X1,X2,X3)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X4,X5) ),
xQyLEz_implies_xQzLEy ).
cnf(c_0_30,hypothesis,
( less_equal(X1,b)
| ~ less_equal(X2,a)
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_31,hypothesis,
less_equal(divide(aQc,X1),a),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( less_equal(divide(X1,X2),X3)
| ~ quotient(X1,X3,X4)
| ~ less_equal(X4,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_33,hypothesis,
( less_equal(X1,b)
| ~ less_equal(X1,divide(aQc,X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,axiom,
( X1 = X2
| ~ less_equal(X1,X2)
| ~ less_equal(X2,X1) ),
less_equal_and_equal ).
cnf(c_0_35,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_36,plain,
( less_equal(divide(X1,X2),X3)
| ~ less_equal(divide(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_21]) ).
cnf(c_0_37,hypothesis,
less_equal(divide(aQc,X1),b),
inference(spm,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_38,axiom,
( less_equal(X7,X8)
| ~ quotient(X1,X2,X3)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X4,X6)
| ~ quotient(X6,X5,X7)
| ~ quotient(X3,X4,X8) ),
quotient_property ).
cnf(c_0_39,axiom,
( less_equal(X4,X5)
| ~ less_equal(X1,X2)
| ~ quotient(X3,X2,X4)
| ~ quotient(X3,X1,X5) ),
xLEy_implies_zQyLEzQx ).
cnf(c_0_40,plain,
( X1 = zero
| ~ less_equal(X1,zero) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,hypothesis,
less_equal(divide(aQc,b),X1),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
( less_equal(X1,X2)
| ~ quotient(X3,X4,zero)
| ~ quotient(X5,X4,X2)
| ~ quotient(X6,X4,X1)
| ~ quotient(X6,X3,X5) ),
inference(spm,[status(thm)],[c_0_38,c_0_25]) ).
cnf(c_0_43,axiom,
( quotient(X1,X2,zero)
| ~ less_equal(X1,X2) ),
quotient_less_equal ).
cnf(c_0_44,plain,
( less_equal(X1,X2)
| ~ quotient(X1,X3,X2)
| ~ less_equal(X3,zero) ),
inference(spm,[status(thm)],[c_0_39,c_0_25]) ).
cnf(c_0_45,axiom,
( X3 = X4
| ~ quotient(X1,X2,X3)
| ~ quotient(X1,X2,X4) ),
well_defined ).
cnf(c_0_46,plain,
( less_equal(divide(X1,X2),X3)
| ~ quotient(X4,X5,X3)
| ~ quotient(X6,X5,X2)
| ~ quotient(X7,X5,X1)
| ~ quotient(X7,X6,X4) ),
inference(spm,[status(thm)],[c_0_38,c_0_21]) ).
cnf(c_0_47,axiom,
quotient(zero,X1,zero),
zero_divide_anything_is_zero ).
cnf(c_0_48,hypothesis,
divide(aQc,b) = zero,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
( less_equal(X1,X2)
| ~ quotient(X3,X4,X2)
| ~ quotient(X5,X4,X1)
| ~ quotient(X5,X6,X3)
| ~ less_equal(X6,X4) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
( less_equal(X1,divide(X1,X2))
| ~ less_equal(X2,zero) ),
inference(spm,[status(thm)],[c_0_44,c_0_21]) ).
cnf(c_0_51,plain,
( X1 = zero
| ~ quotient(X2,X3,X1)
| ~ less_equal(X2,X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_43]) ).
cnf(c_0_52,plain,
( X1 = X2
| ~ quotient(X2,zero,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_25]) ).
cnf(c_0_53,plain,
( less_equal(divide(X1,X2),zero)
| ~ quotient(X3,X4,zero)
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X5,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,hypothesis,
quotient(aQc,b,zero),
inference(spm,[status(thm)],[c_0_21,c_0_48]) ).
cnf(c_0_55,plain,
( less_equal(X1,divide(X2,X3))
| ~ quotient(X4,X3,X1)
| ~ quotient(X4,X5,X2)
| ~ less_equal(X5,X3) ),
inference(spm,[status(thm)],[c_0_49,c_0_21]) ).
cnf(c_0_56,plain,
( less_equal(divide(X1,divide(divide(X1,X2),X3)),X2)
| ~ less_equal(X3,zero) ),
inference(spm,[status(thm)],[c_0_36,c_0_50]) ).
cnf(c_0_57,plain,
( divide(X1,X2) = zero
| ~ less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_21]) ).
cnf(c_0_58,plain,
divide(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_52,c_0_21]) ).
cnf(c_0_59,hypothesis,
( less_equal(divide(X1,X2),zero)
| ~ quotient(b,X3,X2)
| ~ quotient(aQc,X3,X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,hypothesis,
quotient(b,c,bQc),
bQc ).
cnf(c_0_61,hypothesis,
( less_equal(aQc,divide(X1,c))
| ~ quotient(a,X2,X1)
| ~ less_equal(X2,c) ),
inference(spm,[status(thm)],[c_0_55,c_0_17]) ).
cnf(c_0_62,plain,
( less_equal(X1,X2)
| ~ less_equal(divide(X1,X2),X3)
| ~ less_equal(X3,zero) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_63,hypothesis,
( less_equal(divide(X1,bQc),zero)
| ~ quotient(aQc,c,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,hypothesis,
less_equal(aQc,divide(aQc,c)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_17]),c_0_28])]) ).
cnf(c_0_65,hypothesis,
( less_equal(X1,bQc)
| ~ quotient(aQc,c,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_35])]) ).
cnf(c_0_66,hypothesis,
divide(aQc,c) = aQc,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_64]),c_0_24])]) ).
cnf(c_0_67,negated_conjecture,
~ less_equal(aQc,bQc),
prove_aQcLEbQc ).
cnf(c_0_68,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_21]),c_0_66]),c_0_67]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : HEN008-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.32 % Computer : n023.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 : 2400
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon Oct 2 11:35:52 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.45 Running first-order model finding
% 0.18/0.45 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.NeC2zMzNH8/E---3.1_16214.p
% 19.79/2.92 # Version: 3.1pre001
% 19.79/2.92 # Preprocessing class: FSMSSMSSSSSNFFN.
% 19.79/2.92 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.79/2.92 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.79/2.92 # Starting new_bool_3 with 300s (1) cores
% 19.79/2.92 # Starting new_bool_1 with 300s (1) cores
% 19.79/2.92 # Starting sh5l with 300s (1) cores
% 19.79/2.92 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 16293 completed with status 0
% 19.79/2.92 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 19.79/2.92 # Preprocessing class: FSMSSMSSSSSNFFN.
% 19.79/2.92 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.79/2.92 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.79/2.92 # No SInE strategy applied
% 19.79/2.92 # Search class: FHUSM-FFSS22-SFFFFFNN
% 19.79/2.92 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 19.79/2.92 # Starting G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 19.79/2.92 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 19.79/2.92 # Starting new_bool_3 with 136s (1) cores
% 19.79/2.92 # Starting new_bool_1 with 136s (1) cores
% 19.79/2.92 # Starting sh5l with 136s (1) cores
% 19.79/2.92 # G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 16298 completed with status 0
% 19.79/2.92 # Result found by G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 19.79/2.92 # Preprocessing class: FSMSSMSSSSSNFFN.
% 19.79/2.92 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.79/2.92 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.79/2.92 # No SInE strategy applied
% 19.79/2.92 # Search class: FHUSM-FFSS22-SFFFFFNN
% 19.79/2.92 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 19.79/2.92 # Starting G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 19.79/2.92 # Preprocessing time : 0.001 s
% 19.79/2.92 # Presaturation interreduction done
% 19.79/2.92
% 19.79/2.92 # Proof found!
% 19.79/2.92 # SZS status Unsatisfiable
% 19.79/2.92 # SZS output start CNFRefutation
% See solution above
% 19.79/2.92 # Parsed axioms : 20
% 19.79/2.92 # Removed by relevancy pruning/SinE : 0
% 19.79/2.92 # Initial clauses : 20
% 19.79/2.92 # Removed in clause preprocessing : 0
% 19.79/2.92 # Initial clauses in saturation : 20
% 19.79/2.92 # Processed clauses : 41640
% 19.79/2.92 # ...of these trivial : 98
% 19.79/2.92 # ...subsumed : 37928
% 19.79/2.92 # ...remaining for further processing : 3614
% 19.79/2.92 # Other redundant clauses eliminated : 0
% 19.79/2.92 # Clauses deleted for lack of memory : 0
% 19.79/2.92 # Backward-subsumed : 1179
% 19.79/2.92 # Backward-rewritten : 21
% 19.79/2.92 # Generated clauses : 301674
% 19.79/2.92 # ...of the previous two non-redundant : 234178
% 19.79/2.92 # ...aggressively subsumed : 0
% 19.79/2.92 # Contextual simplify-reflections : 20
% 19.79/2.92 # Paramodulations : 301674
% 19.79/2.92 # Factorizations : 0
% 19.79/2.92 # NegExts : 0
% 19.79/2.92 # Equation resolutions : 0
% 19.79/2.92 # Total rewrite steps : 202793
% 19.79/2.92 # Propositional unsat checks : 0
% 19.79/2.92 # Propositional check models : 0
% 19.79/2.92 # Propositional check unsatisfiable : 0
% 19.79/2.92 # Propositional clauses : 0
% 19.79/2.92 # Propositional clauses after purity: 0
% 19.79/2.92 # Propositional unsat core size : 0
% 19.79/2.92 # Propositional preprocessing time : 0.000
% 19.79/2.92 # Propositional encoding time : 0.000
% 19.79/2.92 # Propositional solver time : 0.000
% 19.79/2.92 # Success case prop preproc time : 0.000
% 19.79/2.92 # Success case prop encoding time : 0.000
% 19.79/2.92 # Success case prop solver time : 0.000
% 19.79/2.92 # Current number of processed clauses : 2394
% 19.79/2.92 # Positive orientable unit clauses : 154
% 19.79/2.92 # Positive unorientable unit clauses: 0
% 19.79/2.92 # Negative unit clauses : 245
% 19.79/2.92 # Non-unit-clauses : 1995
% 19.79/2.92 # Current number of unprocessed clauses: 189228
% 19.79/2.92 # ...number of literals in the above : 645199
% 19.79/2.92 # Current number of archived formulas : 0
% 19.79/2.92 # Current number of archived clauses : 1220
% 19.79/2.92 # Clause-clause subsumption calls (NU) : 2270747
% 19.79/2.92 # Rec. Clause-clause subsumption calls : 1169847
% 19.79/2.92 # Non-unit clause-clause subsumptions : 15340
% 19.79/2.92 # Unit Clause-clause subsumption calls : 187592
% 19.79/2.92 # Rewrite failures with RHS unbound : 0
% 19.79/2.92 # BW rewrite match attempts : 1335
% 19.79/2.92 # BW rewrite match successes : 15
% 19.79/2.92 # Condensation attempts : 0
% 19.79/2.92 # Condensation successes : 0
% 19.79/2.92 # Termbank termtop insertions : 3625102
% 19.79/2.92
% 19.79/2.92 # -------------------------------------------------
% 19.79/2.92 # User time : 2.361 s
% 19.79/2.92 # System time : 0.076 s
% 19.79/2.92 # Total time : 2.437 s
% 19.79/2.92 # Maximum resident set size: 1632 pages
% 19.79/2.92
% 19.79/2.92 # -------------------------------------------------
% 19.79/2.92 # User time : 12.043 s
% 19.79/2.92 # System time : 0.183 s
% 19.79/2.92 # Total time : 12.226 s
% 19.79/2.92 # Maximum resident set size: 1688 pages
% 19.79/2.92 % E---3.1 exiting
%------------------------------------------------------------------------------