%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : HEN008-4 : 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 : n015.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 12:45:47 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 37 ( 24 unt; 0 nHn; 20 RR)
% Number of literals : 53 ( 17 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_less_equal2,axiom,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
cnf(less_equal_and_equal,axiom,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
cnf(property_of_divide1,axiom,
( ~ less_equal(divide(X1,X2),X3)
| less_equal(divide(X1,X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide1) ).
cnf(x_divide_x_is_zero,axiom,
divide(X1,X1) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
cnf(quotient_less_equal1,axiom,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
cnf(a_LE_b,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_LE_b) ).
cnf(quotient_property,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_property) ).
cnf(zero_divide_anything_is_zero,axiom,
divide(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
cnf(quotient_smaller_than_numerator,axiom,
less_equal(divide(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_smaller_than_numerator) ).
cnf(prove_a_divide_c_LE_b_divide_c,negated_conjecture,
~ less_equal(divide(a,c),divide(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divide_c_LE_b_divide_c) ).
cnf(c_0_11,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[quotient_less_equal2]) ).
cnf(c_0_12,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[less_equal_and_equal]) ).
cnf(c_0_13,plain,
( ~ less_equal(divide(X1,X2),X3)
| less_equal(divide(X1,X3),X2) ),
inference(fof_simplification,[status(thm)],[property_of_divide1]) ).
cnf(c_0_14,plain,
( divide(X1,X2) != zero
| less_equal(X1,X2) ),
c_0_11 ).
cnf(c_0_15,axiom,
divide(X1,X1) = zero,
x_divide_x_is_zero ).
cnf(c_0_16,plain,
( ~ less_equal(X2,X1)
| ~ less_equal(X1,X2)
| X1 = X2 ),
c_0_12 ).
cnf(c_0_17,axiom,
less_equal(zero,X1),
zero_is_smallest ).
cnf(c_0_18,plain,
( ~ less_equal(divide(X1,X2),X3)
| less_equal(divide(X1,X3),X2) ),
c_0_13 ).
cnf(c_0_19,plain,
less_equal(X1,X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
inference(fof_simplification,[status(thm)],[quotient_less_equal1]) ).
cnf(c_0_21,plain,
( ~ less_equal(X1,zero)
| X1 = zero ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
less_equal(divide(X1,divide(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ~ less_equal(X1,X2)
| divide(X1,X2) = zero ),
c_0_20 ).
cnf(c_0_24,hypothesis,
less_equal(a,b),
a_LE_b ).
cnf(c_0_25,plain,
divide(X1,divide(X1,zero)) = zero,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
quotient_property ).
cnf(c_0_27,hypothesis,
divide(a,b) = zero,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,axiom,
divide(zero,X1) = zero,
zero_divide_anything_is_zero ).
cnf(c_0_29,plain,
less_equal(X1,divide(X1,zero)),
inference(spm,[status(thm)],[c_0_14,c_0_25]) ).
cnf(c_0_30,axiom,
less_equal(divide(X1,X2),X1),
quotient_smaller_than_numerator ).
cnf(c_0_31,negated_conjecture,
~ less_equal(divide(a,c),divide(b,c)),
inference(fof_simplification,[status(thm)],[prove_a_divide_c_LE_b_divide_c]) ).
cnf(c_0_32,hypothesis,
less_equal(divide(divide(a,X1),divide(b,X1)),zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_33,plain,
divide(X1,zero) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_29]),c_0_30])]) ).
cnf(c_0_34,negated_conjecture,
~ less_equal(divide(a,c),divide(b,c)),
c_0_31 ).
cnf(c_0_35,hypothesis,
less_equal(divide(a,X1),divide(b,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_32]),c_0_33]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN008-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:49:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.44 % Version: 3.5.1
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3911187 completed with status 0
% 0.10/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.44 % No SInE strategy applied
% 0.10/0.44 % Search class: FHUSM-FFSF22-SFFFFFNN
% 0.10/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.44 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.10/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.10/0.44 % H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with pid 3911193 completed with status 0
% 0.10/0.44 % Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.44 % No SInE strategy applied
% 0.10/0.44 % Search class: FHUSM-FFSF22-SFFFFFNN
% 0.10/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.44 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.10/0.44 % Preprocessing time : 0.001 s
% 0.10/0.44 % Presaturation interreduction done
% 0.10/0.44
% 0.10/0.44 % Proof found!
% 0.10/0.44 % SZS status Unsatisfiable
% 0.10/0.44 % SZS output start CNFRefutation
% See solution above
% 0.10/0.44 % Parsed axioms : 16
% 0.10/0.44 % Removed by relevancy pruning/SinE : 0
% 0.10/0.44 % Initial clauses : 16
% 0.10/0.44 % Removed in clause preprocessing : 0
% 0.10/0.44 % Initial clauses in saturation : 16
% 0.10/0.44 % Processed clauses : 110
% 0.10/0.44 % ...of these trivial : 3
% 0.10/0.44 % ...subsumed : 35
% 0.10/0.44 % ...remaining for further processing : 72
% 0.10/0.44 % Other redundant clauses eliminated : 0
% 0.10/0.44 % Clauses deleted for lack of memory : 0
% 0.10/0.44 % Backward-subsumed : 1
% 0.10/0.44 % Backward-rewritten : 7
% 0.10/0.44 % Generated clauses : 762
% 0.10/0.44 % ...of the previous two non-redundant : 222
% 0.10/0.44 % ...aggressively subsumed : 0
% 0.10/0.44 % Contextual simplify-reflections : 0
% 0.10/0.44 % Paramodulations : 761
% 0.10/0.44 % Factorizations : 0
% 0.10/0.44 % NegExts : 0
% 0.10/0.44 % Equation resolutions : 1
% 0.10/0.44 % Disequality decompositions : 0
% 0.10/0.44 % Total rewrite steps : 895
% 0.10/0.44 % ...of those cached : 698
% 0.10/0.44 % Propositional unsat checks : 0
% 0.10/0.44 % Propositional check models : 0
% 0.10/0.44 % Propositional check unsatisfiable : 0
% 0.10/0.44 % Propositional clauses : 0
% 0.10/0.44 % Propositional clauses after purity: 0
% 0.10/0.44 % Propositional unsat core size : 0
% 0.10/0.44 % Propositional preprocessing time : 0.000
% 0.10/0.44 % Propositional encoding time : 0.000
% 0.10/0.44 % Propositional solver time : 0.000
% 0.10/0.44 % Success case prop preproc time : 0.000
% 0.10/0.44 % Success case prop encoding time : 0.000
% 0.10/0.44 % Success case prop solver time : 0.000
% 0.10/0.44 % Current number of processed clauses : 48
% 0.10/0.44 % Positive orientable unit clauses : 30
% 0.10/0.44 % Positive unorientable unit clauses: 0
% 0.10/0.44 % Negative unit clauses : 0
% 0.10/0.44 % Non-unit-clauses : 18
% 0.10/0.44 % Current number of unprocessed clauses: 132
% 0.10/0.44 % ...number of literals in the above : 175
% 0.10/0.44 % Current number of archived formulas : 0
% 0.10/0.44 % Current number of archived clauses : 24
% 0.10/0.44 % Clause-clause subsumption calls (NU) : 48
% 0.10/0.44 % Rec. Clause-clause subsumption calls : 48
% 0.10/0.44 % Non-unit clause-clause subsumptions : 36
% 0.10/0.44 % Unit Clause-clause subsumption calls : 4
% 0.10/0.44 % Rewrite failures with RHS unbound : 0
% 0.10/0.44 % BW rewrite match attempts : 22
% 0.10/0.44 % BW rewrite match successes : 4
% 0.10/0.44 % Condensation attempts : 0
% 0.10/0.44 % Condensation successes : 0
% 0.10/0.44 % Termbank termtop insertions : 6077
% 0.10/0.44 % Search garbage collected termcells : 18
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.009 s
% 0.10/0.44 % System time : 0.003 s
% 0.10/0.44 % Total time : 0.012 s
% 0.10/0.44 % Maximum resident set size: 3588 pages
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.040 s
% 0.10/0.44 % System time : 0.010 s
% 0.10/0.44 % Total time : 0.050 s
% 0.10/0.44 % Maximum resident set size: 4864 pages
% 0.10/0.44 % E exiting
%------------------------------------------------------------------------------