%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ANA004-4 : 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 : 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 12:02:43 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 48 ( 5 unt; 19 nHn; 44 RR)
% Number of literals : 112 ( 0 equ; 48 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(less_or_equal_sum_of_halves,axiom,
( ~ less_or_equal(X3,half(X2))
| ~ less_or_equal(X1,half(X2))
| less_or_equal(add(X1,X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_sum_of_halves) ).
cnf(clause_4,hypothesis,
( ~ less_or_equal(absolute(add(X2,negate(a_real_number))),delta_2(X1))
| less_or_equal(absolute(add(g(X2),negate(g(a_real_number)))),X1)
| less_or_equal(X1,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
cnf(absolute_sum_less_or_equal_sum_of_absolutes2,axiom,
( ~ less_or_equal(add(absolute(X1),absolute(X2)),X3)
| less_or_equal(absolute(add(X1,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absolute_sum_less_or_equal_sum_of_absolutes2) ).
cnf(clause_7_1,negated_conjecture,
( ~ less_or_equal(absolute(add(add(f(xs(X1)),negate(f(a_real_number))),add(g(xs(X1)),negate(g(a_real_number))))),epsilon_0)
| less_or_equal(X1,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7_1) ).
cnf(clause_3,hypothesis,
( ~ less_or_equal(absolute(add(X2,negate(a_real_number))),delta_1(X1))
| less_or_equal(absolute(add(f(X2),negate(f(a_real_number)))),X1)
| less_or_equal(X1,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
cnf(minimum3,axiom,
( ~ less_or_equal(X1,minimum(X2,X3))
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum3) ).
cnf(clause_6,hypothesis,
( less_or_equal(absolute(add(xs(X1),negate(a_real_number))),X1)
| less_or_equal(X1,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
cnf(minimum7,axiom,
( ~ less_or_equal(X1,minimum(X2,X3))
| less_or_equal(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum7) ).
cnf(minimum9,axiom,
( ~ less_or_equal(minimum(X1,X2),n0)
| less_or_equal(X2,n0)
| less_or_equal(X1,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum9) ).
cnf(clause_2,hypothesis,
( ~ less_or_equal(delta_2(X1),n0)
| less_or_equal(X1,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
cnf(clause_1,hypothesis,
( ~ less_or_equal(delta_1(X1),n0)
| less_or_equal(X1,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
cnf(zero_and_half,axiom,
( ~ less_or_equal(half(X1),n0)
| less_or_equal(X1,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_and_half) ).
cnf(clause_5,hypothesis,
~ less_or_equal(epsilon_0,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
cnf(c_0_13,plain,
( ~ less_or_equal(X3,half(X2))
| ~ less_or_equal(X1,half(X2))
| less_or_equal(add(X1,X3),X2) ),
inference(fof_simplification,[status(thm)],[less_or_equal_sum_of_halves]) ).
cnf(c_0_14,hypothesis,
( ~ less_or_equal(absolute(add(X2,negate(a_real_number))),delta_2(X1))
| less_or_equal(absolute(add(g(X2),negate(g(a_real_number)))),X1)
| less_or_equal(X1,n0) ),
inference(fof_simplification,[status(thm)],[clause_4]) ).
cnf(c_0_15,plain,
( ~ less_or_equal(add(absolute(X1),absolute(X2)),X3)
| less_or_equal(absolute(add(X1,X2)),X3) ),
inference(fof_simplification,[status(thm)],[absolute_sum_less_or_equal_sum_of_absolutes2]) ).
cnf(c_0_16,plain,
( ~ less_or_equal(X3,half(X2))
| ~ less_or_equal(X1,half(X2))
| less_or_equal(add(X1,X3),X2) ),
c_0_13 ).
cnf(c_0_17,hypothesis,
( ~ less_or_equal(absolute(add(X2,negate(a_real_number))),delta_2(X1))
| less_or_equal(absolute(add(g(X2),negate(g(a_real_number)))),X1)
| less_or_equal(X1,n0) ),
c_0_14 ).
cnf(c_0_18,negated_conjecture,
( ~ less_or_equal(absolute(add(add(f(xs(X1)),negate(f(a_real_number))),add(g(xs(X1)),negate(g(a_real_number))))),epsilon_0)
| less_or_equal(X1,n0) ),
inference(fof_simplification,[status(thm)],[clause_7_1]) ).
cnf(c_0_19,plain,
( ~ less_or_equal(add(absolute(X1),absolute(X2)),X3)
| less_or_equal(absolute(add(X1,X2)),X3) ),
c_0_15 ).
cnf(c_0_20,hypothesis,
( ~ less_or_equal(X1,half(X3))
| ~ less_or_equal(absolute(add(X2,negate(a_real_number))),delta_2(half(X3)))
| less_or_equal(half(X3),n0)
| less_or_equal(add(X1,absolute(add(g(X2),negate(g(a_real_number))))),X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( ~ less_or_equal(absolute(add(add(f(xs(X1)),negate(f(a_real_number))),add(g(xs(X1)),negate(g(a_real_number))))),epsilon_0)
| less_or_equal(X1,n0) ),
c_0_18 ).
cnf(c_0_22,hypothesis,
( ~ less_or_equal(absolute(X1),half(X3))
| ~ less_or_equal(absolute(add(X2,negate(a_real_number))),delta_2(half(X3)))
| less_or_equal(half(X3),n0)
| less_or_equal(absolute(add(X1,add(g(X2),negate(g(a_real_number))))),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,hypothesis,
( ~ less_or_equal(absolute(add(X2,negate(a_real_number))),delta_1(X1))
| less_or_equal(absolute(add(f(X2),negate(f(a_real_number)))),X1)
| less_or_equal(X1,n0) ),
inference(fof_simplification,[status(thm)],[clause_3]) ).
cnf(c_0_24,plain,
( ~ less_or_equal(X1,minimum(X2,X3))
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[minimum3]) ).
cnf(c_0_25,negated_conjecture,
( ~ less_or_equal(absolute(add(xs(X1),negate(a_real_number))),delta_2(half(epsilon_0)))
| ~ less_or_equal(absolute(add(f(xs(X1)),negate(f(a_real_number)))),half(epsilon_0))
| less_or_equal(X1,n0)
| less_or_equal(half(epsilon_0),n0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,hypothesis,
( ~ less_or_equal(absolute(add(X2,negate(a_real_number))),delta_1(X1))
| less_or_equal(absolute(add(f(X2),negate(f(a_real_number)))),X1)
| less_or_equal(X1,n0) ),
c_0_23 ).
cnf(c_0_27,plain,
( ~ less_or_equal(X1,minimum(X2,X3))
| less_or_equal(X1,X2) ),
c_0_24 ).
cnf(c_0_28,hypothesis,
( less_or_equal(absolute(add(xs(X1),negate(a_real_number))),X1)
| less_or_equal(X1,n0) ),
clause_6 ).
cnf(c_0_29,plain,
( ~ less_or_equal(X1,minimum(X2,X3))
| less_or_equal(X1,X3) ),
inference(fof_simplification,[status(thm)],[minimum7]) ).
cnf(c_0_30,hypothesis,
( ~ less_or_equal(absolute(add(xs(X1),negate(a_real_number))),delta_1(half(epsilon_0)))
| ~ less_or_equal(absolute(add(xs(X1),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(X1,n0)
| less_or_equal(half(epsilon_0),n0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,hypothesis,
( less_or_equal(minimum(X1,X2),n0)
| less_or_equal(absolute(add(xs(minimum(X1,X2)),negate(a_real_number))),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( ~ less_or_equal(X1,minimum(X2,X3))
| less_or_equal(X1,X3) ),
c_0_29 ).
cnf(c_0_33,plain,
( ~ less_or_equal(minimum(X1,X2),n0)
| less_or_equal(X2,n0)
| less_or_equal(X1,n0) ),
inference(fof_simplification,[status(thm)],[minimum9]) ).
cnf(c_0_34,hypothesis,
( ~ less_or_equal(absolute(add(xs(minimum(delta_2(half(epsilon_0)),X1)),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(half(epsilon_0),n0)
| less_or_equal(minimum(delta_2(half(epsilon_0)),X1),n0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,hypothesis,
( less_or_equal(minimum(X1,X2),n0)
| less_or_equal(absolute(add(xs(minimum(X1,X2)),negate(a_real_number))),X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_36,hypothesis,
( ~ less_or_equal(delta_2(X1),n0)
| less_or_equal(X1,n0) ),
inference(fof_simplification,[status(thm)],[clause_2]) ).
cnf(c_0_37,hypothesis,
( ~ less_or_equal(delta_1(X1),n0)
| less_or_equal(X1,n0) ),
inference(fof_simplification,[status(thm)],[clause_1]) ).
cnf(c_0_38,plain,
( ~ less_or_equal(half(X1),n0)
| less_or_equal(X1,n0) ),
inference(fof_simplification,[status(thm)],[zero_and_half]) ).
cnf(c_0_39,plain,
( ~ less_or_equal(minimum(X1,X2),n0)
| less_or_equal(X2,n0)
| less_or_equal(X1,n0) ),
c_0_33 ).
cnf(c_0_40,hypothesis,
( less_or_equal(half(epsilon_0),n0)
| less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,hypothesis,
( ~ less_or_equal(delta_2(X1),n0)
| less_or_equal(X1,n0) ),
c_0_36 ).
cnf(c_0_42,hypothesis,
( ~ less_or_equal(delta_1(X1),n0)
| less_or_equal(X1,n0) ),
c_0_37 ).
cnf(c_0_43,hypothesis,
~ less_or_equal(epsilon_0,n0),
inference(fof_simplification,[status(thm)],[clause_5]) ).
cnf(c_0_44,plain,
( ~ less_or_equal(half(X1),n0)
| less_or_equal(X1,n0) ),
c_0_38 ).
cnf(c_0_45,hypothesis,
less_or_equal(half(epsilon_0),n0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42]) ).
cnf(c_0_46,hypothesis,
~ less_or_equal(epsilon_0,n0),
c_0_43 ).
cnf(c_0_47,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA004-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 13:22:53 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.45 % Version: 3.5.1
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.45 % Starting sh5l with 300s (1) cores
% 0.10/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1077417 completed with status 0
% 0.10/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.45 % No SInE strategy applied
% 0.10/0.45 % Search class: FGUNF-FFSF21-MFFFFFNN
% 0.10/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.10/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.10/0.45 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 1077424 completed with status 0
% 0.10/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.45 % No SInE strategy applied
% 0.10/0.45 % Search class: FGUNF-FFSF21-MFFFFFNN
% 0.10/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.10/0.45 % Preprocessing time : 0.001 s
% 0.10/0.45 % Presaturation interreduction done
% 0.10/0.45
% 0.10/0.45 % Proof found!
% 0.10/0.45 % SZS status Unsatisfiable
% 0.10/0.45 % SZS output start CNFRefutation
% See solution above
% 0.10/0.45 % Parsed axioms : 13
% 0.10/0.45 % Removed by relevancy pruning/SinE : 0
% 0.10/0.45 % Initial clauses : 13
% 0.10/0.45 % Removed in clause preprocessing : 0
% 0.10/0.45 % Initial clauses in saturation : 13
% 0.10/0.45 % Processed clauses : 46
% 0.10/0.45 % ...of these trivial : 0
% 0.10/0.45 % ...subsumed : 0
% 0.10/0.45 % ...remaining for further processing : 46
% 0.10/0.45 % Other redundant clauses eliminated : 0
% 0.10/0.45 % Clauses deleted for lack of memory : 0
% 0.10/0.45 % Backward-subsumed : 0
% 0.10/0.45 % Backward-rewritten : 5
% 0.10/0.45 % Generated clauses : 68
% 0.10/0.45 % ...of the previous two non-redundant : 67
% 0.10/0.45 % ...aggressively subsumed : 0
% 0.10/0.45 % Contextual simplify-reflections : 3
% 0.10/0.45 % Paramodulations : 68
% 0.10/0.45 % Factorizations : 0
% 0.10/0.45 % NegExts : 0
% 0.10/0.45 % Equation resolutions : 0
% 0.10/0.45 % Disequality decompositions : 0
% 0.10/0.45 % Total rewrite steps : 5
% 0.10/0.45 % ...of those cached : 4
% 0.10/0.45 % Propositional unsat checks : 0
% 0.10/0.45 % Propositional check models : 0
% 0.10/0.45 % Propositional check unsatisfiable : 0
% 0.10/0.45 % Propositional clauses : 0
% 0.10/0.45 % Propositional clauses after purity: 0
% 0.10/0.45 % Propositional unsat core size : 0
% 0.10/0.45 % Propositional preprocessing time : 0.000
% 0.10/0.45 % Propositional encoding time : 0.000
% 0.10/0.45 % Propositional solver time : 0.000
% 0.10/0.45 % Success case prop preproc time : 0.000
% 0.10/0.45 % Success case prop encoding time : 0.000
% 0.10/0.45 % Success case prop solver time : 0.000
% 0.10/0.45 % Current number of processed clauses : 28
% 0.10/0.45 % Positive orientable unit clauses : 1
% 0.10/0.45 % Positive unorientable unit clauses: 0
% 0.10/0.45 % Negative unit clauses : 1
% 0.10/0.45 % Non-unit-clauses : 26
% 0.10/0.45 % Current number of unprocessed clauses: 47
% 0.10/0.45 % ...number of literals in the above : 155
% 0.10/0.45 % Current number of archived formulas : 0
% 0.10/0.45 % Current number of archived clauses : 18
% 0.10/0.45 % Clause-clause subsumption calls (NU) : 745
% 0.10/0.45 % Rec. Clause-clause subsumption calls : 478
% 0.10/0.45 % Non-unit clause-clause subsumptions : 3
% 0.10/0.45 % Unit Clause-clause subsumption calls : 18
% 0.10/0.45 % Rewrite failures with RHS unbound : 0
% 0.10/0.45 % BW rewrite match attempts : 1
% 0.10/0.45 % BW rewrite match successes : 1
% 0.10/0.45 % Condensation attempts : 0
% 0.10/0.45 % Condensation successes : 0
% 0.10/0.45 % Termbank termtop insertions : 2721
% 0.10/0.45 % Search garbage collected termcells : 36
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.006 s
% 0.10/0.45 % System time : 0.001 s
% 0.10/0.45 % Total time : 0.007 s
% 0.10/0.45 % Maximum resident set size: 3648 pages
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.017 s
% 0.10/0.45 % System time : 0.014 s
% 0.10/0.45 % Total time : 0.030 s
% 0.10/0.45 % Maximum resident set size: 4864 pages
% 0.10/0.45 % E exiting
%------------------------------------------------------------------------------