%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HEN003-2 : 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 : n011.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 12:45:34 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of clauses : 36 ( 15 unt; 0 nHn; 25 RR)
% Number of literals : 80 ( 7 equ; 47 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 89 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(divisor_existence,axiom,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
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(closure,axiom,
quotient(X1,X2,divide(X1,X2)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
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(zero_divide_anything_is_zero,axiom,
quotient(zero,X1,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(prove_x_divide_x_is_zero,negated_conjecture,
~ quotient(x,x,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).
cnf(c_0_8,plain,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
inference(fof_simplification,[status(thm)],[divisor_existence]) ).
cnf(c_0_9,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_10,plain,
( ~ less_equal(X1,X2)
| quotient(X1,X2,zero) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal]) ).
cnf(c_0_11,plain,
( ~ quotient(X1,X2,X3)
| less_equal(X3,X1) ),
c_0_8 ).
cnf(c_0_12,axiom,
quotient(X1,X2,divide(X1,X2)),
closure ).
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_9 ).
cnf(c_0_14,plain,
( ~ less_equal(X1,X2)
| quotient(X1,X2,zero) ),
c_0_10 ).
cnf(c_0_15,plain,
less_equal(divide(X1,X2),X1),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( ~ quotient(X7,X6,X4)
| ~ quotient(X7,X5,X1)
| ~ quotient(X6,X5,X2)
| ~ quotient(X4,X5,X3)
| less_equal(divide(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_17,plain,
quotient(divide(X1,X2),X1,zero),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( ~ quotient(X3,X5,X1)
| ~ quotient(X4,X5,X2)
| ~ quotient(X3,X4,divide(X5,X6))
| less_equal(divide(X1,X2),zero) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_20,plain,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[less_equal_quotient]) ).
cnf(c_0_21,plain,
( ~ quotient(X4,X4,X1)
| ~ quotient(X3,X4,X2)
| less_equal(divide(X1,X2),zero) ),
inference(spm,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_22,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_19 ).
cnf(c_0_23,plain,
( ~ quotient(X1,X2,zero)
| less_equal(X1,X2) ),
c_0_20 ).
cnf(c_0_24,plain,
( ~ quotient(X2,X2,X1)
| less_equal(divide(X1,zero),zero) ),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_25,plain,
( ~ less_equal(X1,X2)
| ~ quotient(X2,X1,zero)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
less_equal(divide(divide(X1,X1),zero),zero),
inference(spm,[status(thm)],[c_0_24,c_0_12]) ).
cnf(c_0_27,axiom,
quotient(zero,X1,zero),
zero_divide_anything_is_zero ).
cnf(c_0_28,plain,
divide(divide(X1,X1),zero) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_29,plain,
( ~ quotient(X1,X2,zero)
| ~ quotient(X2,X1,zero)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_30,plain,
quotient(divide(X1,X1),zero,zero),
inference(spm,[status(thm)],[c_0_12,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
~ quotient(x,x,zero),
inference(fof_simplification,[status(thm)],[prove_x_divide_x_is_zero]) ).
cnf(c_0_32,plain,
divide(X1,X1) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27])]) ).
cnf(c_0_33,negated_conjecture,
~ quotient(x,x,zero),
c_0_31 ).
cnf(c_0_34,plain,
quotient(X1,X1,zero),
inference(spm,[status(thm)],[c_0_12,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n011.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 20 20:45:26 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.43 % Version: 3.5.1
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.43 % Starting sh5l with 300s (1) cores
% 0.12/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 147608 completed with status 0
% 0.12/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.43 % No SInE strategy applied
% 0.12/0.43 % Search class: FHUSM-FFSF22-SFFFFFNN
% 0.12/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.43 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.12/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.12/0.43 % SubtermCWHack with pid 147613 completed with status 0
% 0.12/0.43 % Result found by SubtermCWHack
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.43 % No SInE strategy applied
% 0.12/0.43 % Search class: FHUSM-FFSF22-SFFFFFNN
% 0.12/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.43 % Preprocessing time : 0.001 s
% 0.12/0.43
% 0.12/0.43 % Proof found!
% 0.12/0.43 % SZS status Unsatisfiable
% 0.12/0.43 % SZS output start CNFRefutation
% See solution above
% 0.12/0.43 % Parsed axioms : 12
% 0.12/0.43 % Removed by relevancy pruning/SinE : 0
% 0.12/0.43 % Initial clauses : 12
% 0.12/0.43 % Removed in clause preprocessing : 0
% 0.12/0.43 % Initial clauses in saturation : 12
% 0.12/0.43 % Processed clauses : 51
% 0.12/0.43 % ...of these trivial : 0
% 0.12/0.43 % ...subsumed : 13
% 0.12/0.43 % ...remaining for further processing : 38
% 0.12/0.43 % Other redundant clauses eliminated : 0
% 0.12/0.43 % Clauses deleted for lack of memory : 0
% 0.12/0.43 % Backward-subsumed : 0
% 0.12/0.43 % Backward-rewritten : 4
% 0.12/0.43 % Generated clauses : 116
% 0.12/0.43 % ...of the previous two non-redundant : 63
% 0.12/0.43 % ...aggressively subsumed : 0
% 0.12/0.43 % Contextual simplify-reflections : 0
% 0.12/0.43 % Paramodulations : 116
% 0.12/0.43 % Factorizations : 0
% 0.12/0.43 % NegExts : 0
% 0.12/0.43 % Equation resolutions : 0
% 0.12/0.43 % Disequality decompositions : 0
% 0.12/0.43 % Total rewrite steps : 59
% 0.12/0.43 % ...of those cached : 38
% 0.12/0.43 % Propositional unsat checks : 0
% 0.12/0.43 % Propositional check models : 0
% 0.12/0.43 % Propositional check unsatisfiable : 0
% 0.12/0.43 % Propositional clauses : 0
% 0.12/0.43 % Propositional clauses after purity: 0
% 0.12/0.43 % Propositional unsat core size : 0
% 0.12/0.43 % Propositional preprocessing time : 0.000
% 0.12/0.43 % Propositional encoding time : 0.000
% 0.12/0.43 % Propositional solver time : 0.000
% 0.12/0.43 % Success case prop preproc time : 0.000
% 0.12/0.43 % Success case prop encoding time : 0.000
% 0.12/0.43 % Success case prop solver time : 0.000
% 0.12/0.43 % Current number of processed clauses : 34
% 0.12/0.43 % Positive orientable unit clauses : 12
% 0.12/0.43 % Positive unorientable unit clauses: 0
% 0.12/0.43 % Negative unit clauses : 0
% 0.12/0.43 % Non-unit-clauses : 22
% 0.12/0.43 % Current number of unprocessed clauses: 24
% 0.12/0.43 % ...number of literals in the above : 62
% 0.12/0.43 % Current number of archived formulas : 0
% 0.12/0.43 % Current number of archived clauses : 4
% 0.12/0.43 % Clause-clause subsumption calls (NU) : 114
% 0.12/0.43 % Rec. Clause-clause subsumption calls : 86
% 0.12/0.43 % Non-unit clause-clause subsumptions : 13
% 0.12/0.43 % Unit Clause-clause subsumption calls : 4
% 0.12/0.43 % Rewrite failures with RHS unbound : 0
% 0.12/0.43 % BW rewrite match attempts : 41
% 0.12/0.43 % BW rewrite match successes : 3
% 0.12/0.43 % Condensation attempts : 0
% 0.12/0.43 % Condensation successes : 0
% 0.12/0.43 % Termbank termtop insertions : 1389
% 0.12/0.43 % Search garbage collected termcells : 30
% 0.12/0.43
% 0.12/0.43 % -------------------------------------------------
% 0.12/0.43 % User time : 0.005 s
% 0.12/0.43 % System time : 0.003 s
% 0.12/0.43 % Total time : 0.008 s
% 0.12/0.43 % Maximum resident set size: 3640 pages
% 0.12/0.43
% 0.12/0.43 % -------------------------------------------------
% 0.12/0.43 % User time : 0.021 s
% 0.12/0.43 % System time : 0.012 s
% 0.12/0.43 % Total time : 0.033 s
% 0.12/0.43 % Maximum resident set size: 4608 pages
% 0.12/0.43 % E exiting
%------------------------------------------------------------------------------