%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HEN005-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:45:35 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 37 ( 21 unt; 0 nHn; 29 RR)
% Number of literals : 74 ( 4 equ; 40 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(quotient_less_equal,axiom,
( ~ less_equal(X1,X2)
| quotient(X1,X2,zero) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
cnf(x_divde_zero_is_x,axiom,
quotient(X1,zero,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
cnf(yLEz,hypothesis,
less_equal(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',yLEz) ).
cnf(zero_divide_anything_is_zero,axiom,
quotient(zero,X1,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(xLEy,hypothesis,
less_equal(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xLEy) ).
cnf(less_equal_and_equal,axiom,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
cnf(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(less_equal_quotient,axiom,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(prove_transitivity_of_less_equal,negated_conjecture,
~ less_equal(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_less_equal) ).
cnf(c_0_11,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_12,plain,
( ~ less_equal(X1,X2)
| quotient(X1,X2,zero) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal]) ).
cnf(c_0_13,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_11 ).
cnf(c_0_14,axiom,
quotient(X1,zero,X1),
x_divde_zero_is_x ).
cnf(c_0_15,plain,
( ~ less_equal(X1,X2)
| quotient(X1,X2,zero) ),
c_0_12 ).
cnf(c_0_16,hypothesis,
less_equal(y,z),
yLEz ).
cnf(c_0_17,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_13,c_0_14]) ).
cnf(c_0_18,hypothesis,
quotient(y,z,zero),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,hypothesis,
( ~ quotient(X4,y,X3)
| ~ quotient(X4,z,X1)
| ~ quotient(X3,z,X2)
| less_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,axiom,
quotient(zero,X1,zero),
zero_divide_anything_is_zero ).
cnf(c_0_21,hypothesis,
less_equal(x,y),
xLEy ).
cnf(c_0_22,hypothesis,
( ~ quotient(X2,z,X1)
| ~ quotient(X2,y,zero)
| less_equal(X1,zero) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,hypothesis,
quotient(x,y,zero),
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
cnf(c_0_24,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_25,hypothesis,
( ~ quotient(x,z,X1)
| less_equal(X1,zero) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
cnf(c_0_27,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_24 ).
cnf(c_0_28,hypothesis,
less_equal(divide(x,z),zero),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_30,plain,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[less_equal_quotient]) ).
cnf(c_0_31,hypothesis,
divide(x,z) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_32,negated_conjecture,
~ less_equal(x,z),
inference(fof_simplification,[status(thm)],[prove_transitivity_of_less_equal]) ).
cnf(c_0_33,plain,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
c_0_30 ).
cnf(c_0_34,hypothesis,
quotient(x,z,zero),
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
~ less_equal(x,z),
c_0_32 ).
cnf(c_0_36,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:46:24 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.43 % Version: 3.5.1
% 0.09/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.43 % Starting sh5l with 300s (1) cores
% 0.09/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3577866 completed with status 0
% 0.09/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.09/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.43 % No SInE strategy applied
% 0.09/0.43 % Search class: FHUSM-FFSF22-SFFFFFNN
% 0.09/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.09/0.43 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.09/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.09/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.09/0.43 % H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with pid 3577873 completed with status 0
% 0.09/0.43 % Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S
% 0.09/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.43 % No SInE strategy applied
% 0.09/0.43 % Search class: FHUSM-FFSF22-SFFFFFNN
% 0.09/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.09/0.43 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.09/0.43 % Preprocessing time : 0.001 s
% 0.09/0.43 % Presaturation interreduction done
% 0.09/0.43
% 0.09/0.43 % Proof found!
% 0.09/0.43 % SZS status Unsatisfiable
% 0.09/0.43 % SZS output start CNFRefutation
% See solution above
% 0.09/0.43 % Parsed axioms : 16
% 0.09/0.43 % Removed by relevancy pruning/SinE : 0
% 0.09/0.43 % Initial clauses : 16
% 0.09/0.43 % Removed in clause preprocessing : 0
% 0.09/0.43 % Initial clauses in saturation : 16
% 0.09/0.43 % Processed clauses : 112
% 0.09/0.43 % ...of these trivial : 2
% 0.09/0.43 % ...subsumed : 26
% 0.09/0.43 % ...remaining for further processing : 84
% 0.09/0.43 % Other redundant clauses eliminated : 0
% 0.09/0.43 % Clauses deleted for lack of memory : 0
% 0.09/0.43 % Backward-subsumed : 0
% 0.09/0.43 % Backward-rewritten : 2
% 0.09/0.43 % Generated clauses : 298
% 0.09/0.43 % ...of the previous two non-redundant : 116
% 0.09/0.43 % ...aggressively subsumed : 0
% 0.09/0.43 % Contextual simplify-reflections : 0
% 0.09/0.43 % Paramodulations : 298
% 0.09/0.43 % Factorizations : 0
% 0.09/0.43 % NegExts : 0
% 0.09/0.43 % Equation resolutions : 0
% 0.09/0.43 % Disequality decompositions : 0
% 0.09/0.43 % Total rewrite steps : 233
% 0.09/0.43 % ...of those cached : 185
% 0.09/0.43 % Propositional unsat checks : 0
% 0.09/0.43 % Propositional check models : 0
% 0.09/0.43 % Propositional check unsatisfiable : 0
% 0.09/0.43 % Propositional clauses : 0
% 0.09/0.43 % Propositional clauses after purity: 0
% 0.09/0.43 % Propositional unsat core size : 0
% 0.09/0.43 % Propositional preprocessing time : 0.000
% 0.09/0.43 % Propositional encoding time : 0.000
% 0.09/0.43 % Propositional solver time : 0.000
% 0.09/0.43 % Success case prop preproc time : 0.000
% 0.09/0.43 % Success case prop encoding time : 0.000
% 0.09/0.43 % Success case prop solver time : 0.000
% 0.09/0.43 % Current number of processed clauses : 66
% 0.09/0.43 % Positive orientable unit clauses : 25
% 0.09/0.43 % Positive unorientable unit clauses: 0
% 0.09/0.43 % Negative unit clauses : 1
% 0.09/0.43 % Non-unit-clauses : 40
% 0.09/0.43 % Current number of unprocessed clauses: 33
% 0.09/0.43 % ...number of literals in the above : 102
% 0.09/0.43 % Current number of archived formulas : 0
% 0.09/0.43 % Current number of archived clauses : 18
% 0.09/0.43 % Clause-clause subsumption calls (NU) : 448
% 0.09/0.43 % Rec. Clause-clause subsumption calls : 390
% 0.09/0.43 % Non-unit clause-clause subsumptions : 26
% 0.09/0.43 % Unit Clause-clause subsumption calls : 2
% 0.09/0.43 % Rewrite failures with RHS unbound : 0
% 0.09/0.43 % BW rewrite match attempts : 27
% 0.09/0.43 % BW rewrite match successes : 2
% 0.09/0.43 % Condensation attempts : 0
% 0.09/0.43 % Condensation successes : 0
% 0.09/0.43 % Termbank termtop insertions : 3005
% 0.09/0.43 % Search garbage collected termcells : 30
% 0.09/0.43
% 0.09/0.43 % -------------------------------------------------
% 0.09/0.43 % User time : 0.005 s
% 0.09/0.43 % System time : 0.003 s
% 0.09/0.43 % Total time : 0.008 s
% 0.09/0.43 % Maximum resident set size: 3640 pages
% 0.09/0.43
% 0.09/0.43 % -------------------------------------------------
% 0.09/0.43 % User time : 0.021 s
% 0.09/0.43 % System time : 0.015 s
% 0.09/0.43 % Total time : 0.036 s
% 0.09/0.43 % Maximum resident set size: 4864 pages
% 0.09/0.43 % E exiting
%------------------------------------------------------------------------------