%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HEN010-7 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:45:40 PM UTC 2026
% Result : Unsatisfiable 0.26s 0.65s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 51 ( 24 unt; 0 nHn; 44 RR)
% Number of literals : 112 ( 8 equ; 66 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 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 : 106 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(less_equal_quotient,axiom,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(xQyLEz_implies_xQzLEy,axiom,
( ~ quotient(X1,X4,X5)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X2,X3)
| less_equal(X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).
cnf(x_divide_x_is_zero,axiom,
quotient(X1,X1,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQa) ).
cnf(xLEy_implies_zQyLEzQx,axiom,
( ~ quotient(X3,X1,X5)
| ~ quotient(X3,X2,X4)
| ~ less_equal(X1,X2)
| less_equal(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy_implies_zQyLEzQx) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_a) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(less_equal_and_equal,axiom,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
cnf(quotient_property,axiom,
( ~ quotient(X3,X4,X8)
| ~ quotient(X6,X5,X7)
| ~ quotient(X1,X4,X6)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X2,X3)
| less_equal(X7,X8) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(divisor_existence,axiom,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(x_divde_zero_is_x,axiom,
quotient(X1,zero,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
cnf(identity_divide_idQ_idQa,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
cnf(prove_idQa_equals_idQa_Q__idQ_idQa,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_idQa_equals_idQa_Q__idQ_idQa) ).
cnf(c_0_13,plain,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[less_equal_quotient]) ).
cnf(c_0_14,plain,
( ~ quotient(X1,X4,X5)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X2,X3)
| less_equal(X5,X2) ),
inference(fof_simplification,[status(thm)],[xQyLEz_implies_xQzLEy]) ).
cnf(c_0_15,plain,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
c_0_13 ).
cnf(c_0_16,axiom,
quotient(X1,X1,zero),
x_divide_x_is_zero ).
cnf(c_0_17,plain,
( ~ quotient(X1,X4,X5)
| ~ less_equal(X3,X4)
| ~ quotient(X1,X2,X3)
| less_equal(X5,X2) ),
c_0_14 ).
cnf(c_0_18,plain,
less_equal(X1,X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( ~ quotient(X3,X2,X4)
| ~ quotient(X3,X4,X1)
| less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,hypothesis,
quotient(identity,idQa,idQ_idQa),
identity_divide_idQa ).
cnf(c_0_21,plain,
( ~ quotient(X3,X1,X5)
| ~ quotient(X3,X2,X4)
| ~ less_equal(X1,X2)
| less_equal(X4,X5) ),
inference(fof_simplification,[status(thm)],[xLEy_implies_zQyLEzQx]) ).
cnf(c_0_22,hypothesis,
( ~ quotient(identity,X1,idQa)
| less_equal(idQ_idQa,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,hypothesis,
quotient(identity,a,idQa),
identity_divide_a ).
cnf(c_0_24,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_25,plain,
( ~ quotient(X3,X1,X5)
| ~ quotient(X3,X2,X4)
| ~ less_equal(X1,X2)
| less_equal(X4,X5) ),
c_0_21 ).
cnf(c_0_26,hypothesis,
less_equal(idQ_idQa,a),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_28,plain,
( ~ quotient(X1,X3,X2)
| less_equal(divide(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_29,hypothesis,
( ~ quotient(X3,idQ_idQa,X2)
| ~ quotient(X3,a,X1)
| less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( ~ quotient(X3,X4,X8)
| ~ quotient(X6,X5,X7)
| ~ quotient(X1,X4,X6)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X2,X3)
| less_equal(X7,X8) ),
inference(fof_simplification,[status(thm)],[quotient_property]) ).
cnf(c_0_31,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_27 ).
cnf(c_0_32,hypothesis,
less_equal(divide(identity,idQ_idQa),idQa),
inference(spm,[status(thm)],[c_0_28,c_0_20]) ).
cnf(c_0_33,hypothesis,
( ~ quotient(identity,idQ_idQa,X1)
| less_equal(idQa,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_34,plain,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
inference(fof_simplification,[status(thm)],[divisor_existence]) ).
cnf(c_0_35,plain,
( ~ quotient(X3,X4,X8)
| ~ quotient(X6,X5,X7)
| ~ quotient(X1,X4,X6)
| ~ quotient(X2,X4,X5)
| ~ quotient(X1,X2,X3)
| less_equal(X7,X8) ),
c_0_30 ).
cnf(c_0_36,axiom,
quotient(X1,zero,X1),
x_divde_zero_is_x ).
cnf(c_0_37,hypothesis,
( ~ less_equal(idQa,divide(identity,idQ_idQa))
| divide(identity,idQ_idQa) = idQa ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,hypothesis,
less_equal(idQa,divide(identity,idQ_idQa)),
inference(spm,[status(thm)],[c_0_33,c_0_24]) ).
cnf(c_0_39,plain,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
c_0_34 ).
cnf(c_0_40,hypothesis,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
identity_divide_idQ_idQa ).
cnf(c_0_41,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
inference(fof_simplification,[status(thm)],[prove_idQa_equals_idQa_Q__idQ_idQa]) ).
cnf(c_0_42,plain,
( ~ quotient(X6,X3,X5)
| ~ quotient(X6,X4,X1)
| ~ quotient(X5,X4,X2)
| ~ quotient(X3,X4,zero)
| less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,hypothesis,
divide(identity,idQ_idQa) = idQa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_44,hypothesis,
less_equal(idQa_Q__idQ_idQa,idQa),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
c_0_41 ).
cnf(c_0_46,hypothesis,
( ~ quotient(X3,X2,idQa)
| ~ quotient(X3,idQ_idQa,X1)
| ~ quotient(X2,idQ_idQa,zero)
| less_equal(X1,idQa_Q__idQ_idQa) ),
inference(spm,[status(thm)],[c_0_42,c_0_40]) ).
cnf(c_0_47,hypothesis,
quotient(identity,idQ_idQa,idQa),
inference(spm,[status(thm)],[c_0_24,c_0_43]) ).
cnf(c_0_48,hypothesis,
~ less_equal(idQa,idQa_Q__idQ_idQa),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_44]),c_0_45]) ).
cnf(c_0_49,hypothesis,
( ~ quotient(identity,X1,idQa)
| ~ quotient(X1,idQ_idQa,zero) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_50,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_16]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : HEN010-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.40 % Computer : n010.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Sun Sep 20 20:47:10 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 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
% 0.26/0.65 % Version: 3.5.1
% 0.26/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.65 % Starting sh5l with 300s (1) cores
% 0.26/0.65 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3491925 completed with status 0
% 0.26/0.65 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.26/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.65 % No SInE strategy applied
% 0.26/0.65 % Search class: FHUSM-FFSS22-SFFFFFNN
% 0.26/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.26/0.65 % Starting G-E--_208_C12_00_F1_SE_CS_PI_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.26/0.65 % Starting new_bool_3 with 136s (1) cores
% 0.26/0.65 % Starting new_bool_1 with 136s (1) cores
% 0.26/0.65 % new_bool_1 with pid 3491933 completed with status 0
% 0.26/0.65 % Result found by new_bool_1
% 0.26/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.65 % No SInE strategy applied
% 0.26/0.65 % Search class: FHUSM-FFSS22-SFFFFFNN
% 0.26/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.26/0.65 % Starting G-E--_208_C12_00_F1_SE_CS_PI_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.26/0.65 % Starting new_bool_3 with 136s (1) cores
% 0.26/0.65 % Starting new_bool_1 with 136s (1) cores
% 0.26/0.65 % Preprocessing time : 0.002 s
% 0.26/0.65 % Presaturation interreduction done
% 0.26/0.65
% 0.26/0.65 % Proof found!
% 0.26/0.65 % SZS status Unsatisfiable
% 0.26/0.65 % SZS output start CNFRefutation
% See solution above
% 0.26/0.65 % Parsed axioms : 21
% 0.26/0.65 % Removed by relevancy pruning/SinE : 0
% 0.26/0.65 % Initial clauses : 21
% 0.26/0.65 % Removed in clause preprocessing : 0
% 0.26/0.65 % Initial clauses in saturation : 21
% 0.26/0.65 % Processed clauses : 1152
% 0.26/0.65 % ...of these trivial : 23
% 0.26/0.65 % ...subsumed : 671
% 0.26/0.65 % ...remaining for further processing : 458
% 0.26/0.65 % Other redundant clauses eliminated : 0
% 0.26/0.65 % Clauses deleted for lack of memory : 0
% 0.26/0.65 % Backward-subsumed : 13
% 0.26/0.65 % Backward-rewritten : 14
% 0.26/0.65 % Generated clauses : 3417
% 0.26/0.65 % ...of the previous two non-redundant : 1958
% 0.26/0.65 % ...aggressively subsumed : 0
% 0.26/0.65 % Contextual simplify-reflections : 0
% 0.26/0.65 % Paramodulations : 3417
% 0.26/0.65 % Factorizations : 0
% 0.26/0.65 % NegExts : 0
% 0.26/0.65 % Equation resolutions : 0
% 0.26/0.65 % Disequality decompositions : 0
% 0.26/0.65 % Total rewrite steps : 2047
% 0.26/0.65 % ...of those cached : 1781
% 0.26/0.65 % Propositional unsat checks : 0
% 0.26/0.65 % Propositional check models : 0
% 0.26/0.65 % Propositional check unsatisfiable : 0
% 0.26/0.65 % Propositional clauses : 0
% 0.26/0.65 % Propositional clauses after purity: 0
% 0.26/0.65 % Propositional unsat core size : 0
% 0.26/0.65 % Propositional preprocessing time : 0.000
% 0.26/0.65 % Propositional encoding time : 0.000
% 0.26/0.65 % Propositional solver time : 0.000
% 0.26/0.65 % Success case prop preproc time : 0.000
% 0.26/0.65 % Success case prop encoding time : 0.000
% 0.26/0.65 % Success case prop solver time : 0.000
% 0.26/0.65 % Current number of processed clauses : 410
% 0.26/0.65 % Positive orientable unit clauses : 103
% 0.26/0.65 % Positive unorientable unit clauses: 0
% 0.26/0.65 % Negative unit clauses : 2
% 0.26/0.65 % Non-unit-clauses : 305
% 0.26/0.65 % Current number of unprocessed clauses: 817
% 0.26/0.65 % ...number of literals in the above : 2156
% 0.26/0.65 % Current number of archived formulas : 0
% 0.26/0.65 % Current number of archived clauses : 48
% 0.26/0.65 % Clause-clause subsumption calls (NU) : 29934
% 0.26/0.65 % Rec. Clause-clause subsumption calls : 23107
% 0.26/0.65 % Non-unit clause-clause subsumptions : 679
% 0.26/0.65 % Unit Clause-clause subsumption calls : 1
% 0.26/0.65 % Rewrite failures with RHS unbound : 0
% 0.26/0.65 % BW rewrite match attempts : 57
% 0.26/0.65 % BW rewrite match successes : 3
% 0.26/0.65 % Condensation attempts : 0
% 0.26/0.65 % Condensation successes : 0
% 0.26/0.65 % Termbank termtop insertions : 37701
% 0.26/0.65 % Search garbage collected termcells : 54
% 0.26/0.65
% 0.26/0.65 % -------------------------------------------------
% 0.26/0.65 % User time : 0.116 s
% 0.26/0.65 % System time : 0.011 s
% 0.26/0.65 % Total time : 0.127 s
% 0.26/0.65 % Maximum resident set size: 3644 pages
% 0.26/0.65
% 0.26/0.65 % -------------------------------------------------
% 0.26/0.65 % User time : 0.405 s
% 0.26/0.65 % System time : 0.030 s
% 0.26/0.65 % Total time : 0.434 s
% 0.26/0.65 % Maximum resident set size: 4864 pages
% 0.26/0.65 % E exiting
%------------------------------------------------------------------------------