%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM022-1 : 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 : n007.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 01:44:16 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 29 ( 10 unt; 5 nHn; 29 RR)
% Number of literals : 57 ( 0 equ; 26 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(less_lemma,axiom,
( ~ less(X1,X2)
| equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-1.ax',less_lemma) ).
cnf(transitivity,axiom,
( ~ equalish(X3,X1)
| ~ equalish(X1,X2)
| equalish(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
cnf(a_less_than_b,hypothesis,
less(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_less_than_b) ).
cnf(divides_only_less_or_equal,axiom,
( ~ divides(X1,X2)
| equalish(X1,X2)
| less(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-2.ax',divides_only_less_or_equal) ).
cnf(b_divides_d,hypothesis,
divides(b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_divides_d) ).
cnf(transitivity_of_less,axiom,
( ~ less(X3,X1)
| ~ less(X1,X2)
| less(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-1.ax',transitivity_of_less) ).
cnf(smaller_number,axiom,
( ~ equalish(add(successor(X1),X2),X3)
| less(X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-1.ax',smaller_number) ).
cnf(prove_a_less_than_d,negated_conjecture,
~ less(a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_less_than_d) ).
cnf(c_0_8,plain,
( ~ less(X1,X2)
| equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2) ),
inference(fof_simplification,[status(thm)],[less_lemma]) ).
cnf(c_0_9,plain,
( ~ equalish(X3,X1)
| ~ equalish(X1,X2)
| equalish(X3,X2) ),
inference(fof_simplification,[status(thm)],[transitivity]) ).
cnf(c_0_10,plain,
( ~ less(X1,X2)
| equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2) ),
c_0_8 ).
cnf(c_0_11,hypothesis,
less(a,b),
a_less_than_b ).
cnf(c_0_12,plain,
( ~ divides(X1,X2)
| equalish(X1,X2)
| less(X1,X2) ),
inference(fof_simplification,[status(thm)],[divides_only_less_or_equal]) ).
cnf(c_0_13,plain,
( ~ equalish(X3,X1)
| ~ equalish(X1,X2)
| equalish(X3,X2) ),
c_0_9 ).
cnf(c_0_14,hypothesis,
equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),b),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( ~ divides(X1,X2)
| equalish(X1,X2)
| less(X1,X2) ),
c_0_12 ).
cnf(c_0_16,hypothesis,
divides(b,d),
b_divides_d ).
cnf(c_0_17,plain,
( ~ less(X3,X1)
| ~ less(X1,X2)
| less(X3,X2) ),
inference(fof_simplification,[status(thm)],[transitivity_of_less]) ).
cnf(c_0_18,plain,
( ~ equalish(add(successor(X1),X2),X3)
| less(X2,X3) ),
inference(fof_simplification,[status(thm)],[smaller_number]) ).
cnf(c_0_19,hypothesis,
( ~ equalish(b,X1)
| equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,hypothesis,
( less(b,d)
| equalish(b,d) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
~ less(a,d),
inference(fof_simplification,[status(thm)],[prove_a_less_than_d]) ).
cnf(c_0_22,plain,
( ~ less(X3,X1)
| ~ less(X1,X2)
| less(X3,X2) ),
c_0_17 ).
cnf(c_0_23,plain,
( ~ equalish(add(successor(X1),X2),X3)
| less(X2,X3) ),
c_0_18 ).
cnf(c_0_24,hypothesis,
( less(b,d)
| equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),d) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
~ less(a,d),
c_0_21 ).
cnf(c_0_26,hypothesis,
( ~ less(b,X1)
| less(a,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_11]) ).
cnf(c_0_27,hypothesis,
less(b,d),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_28,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 01:57:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.40 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
% 0.13/0.41 % Version: 3.5.1
% 0.13/0.41 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.41 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.41 % Starting sh5l with 300s (1) cores
% 0.13/0.41 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 4126747 completed with status 0
% 0.13/0.41 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.13/0.41 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.41 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.41 % No SInE strategy applied
% 0.13/0.41 % Search class: FGUNF-FFSF21-MFFFFFNN
% 0.13/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.41 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.13/0.41 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.41 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.41 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.41 % new_bool_3 with pid 4126755 completed with status 0
% 0.13/0.41 % Result found by new_bool_3
% 0.13/0.41 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.41 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.41 % No SInE strategy applied
% 0.13/0.41 % Search class: FGUNF-FFSF21-MFFFFFNN
% 0.13/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.41 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.13/0.41 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.41 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.41 % Preprocessing time : 0.001 s
% 0.13/0.41 % Presaturation interreduction done
% 0.13/0.41
% 0.13/0.41 % Proof found!
% 0.13/0.41 % SZS status Unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation
% See solution above
% 0.13/0.41 % Parsed axioms : 10
% 0.13/0.41 % Removed by relevancy pruning/SinE : 0
% 0.13/0.41 % Initial clauses : 10
% 0.13/0.41 % Removed in clause preprocessing : 0
% 0.13/0.41 % Initial clauses in saturation : 10
% 0.13/0.41 % Processed clauses : 29
% 0.13/0.41 % ...of these trivial : 0
% 0.13/0.41 % ...subsumed : 0
% 0.13/0.41 % ...remaining for further processing : 29
% 0.13/0.41 % Other redundant clauses eliminated : 0
% 0.13/0.41 % Clauses deleted for lack of memory : 0
% 0.13/0.41 % Backward-subsumed : 0
% 0.13/0.41 % Backward-rewritten : 3
% 0.13/0.41 % Generated clauses : 19
% 0.13/0.41 % ...of the previous two non-redundant : 13
% 0.13/0.41 % ...aggressively subsumed : 0
% 0.13/0.41 % Contextual simplify-reflections : 0
% 0.13/0.41 % Paramodulations : 19
% 0.13/0.41 % Factorizations : 0
% 0.13/0.41 % NegExts : 0
% 0.13/0.41 % Equation resolutions : 0
% 0.13/0.41 % Disequality decompositions : 0
% 0.13/0.41 % Total rewrite steps : 8
% 0.13/0.41 % ...of those cached : 4
% 0.13/0.41 % Propositional unsat checks : 0
% 0.13/0.41 % Propositional check models : 0
% 0.13/0.41 % Propositional check unsatisfiable : 0
% 0.13/0.41 % Propositional clauses : 0
% 0.13/0.41 % Propositional clauses after purity: 0
% 0.13/0.41 % Propositional unsat core size : 0
% 0.13/0.41 % Propositional preprocessing time : 0.000
% 0.13/0.41 % Propositional encoding time : 0.000
% 0.13/0.41 % Propositional solver time : 0.000
% 0.13/0.41 % Success case prop preproc time : 0.000
% 0.13/0.41 % Success case prop encoding time : 0.000
% 0.13/0.41 % Success case prop solver time : 0.000
% 0.13/0.41 % Current number of processed clauses : 16
% 0.13/0.41 % Positive orientable unit clauses : 6
% 0.13/0.41 % Positive unorientable unit clauses: 0
% 0.13/0.41 % Negative unit clauses : 1
% 0.13/0.41 % Non-unit-clauses : 9
% 0.13/0.41 % Current number of unprocessed clauses: 2
% 0.13/0.41 % ...number of literals in the above : 5
% 0.13/0.41 % Current number of archived formulas : 0
% 0.13/0.41 % Current number of archived clauses : 13
% 0.13/0.41 % Clause-clause subsumption calls (NU) : 5
% 0.13/0.41 % Rec. Clause-clause subsumption calls : 4
% 0.13/0.41 % Non-unit clause-clause subsumptions : 0
% 0.13/0.41 % Unit Clause-clause subsumption calls : 0
% 0.13/0.41 % Rewrite failures with RHS unbound : 0
% 0.13/0.41 % BW rewrite match attempts : 1
% 0.13/0.41 % BW rewrite match successes : 1
% 0.13/0.41 % Condensation attempts : 0
% 0.13/0.41 % Condensation successes : 0
% 0.13/0.41 % Termbank termtop insertions : 538
% 0.13/0.41 % Search garbage collected termcells : 20
% 0.13/0.41
% 0.13/0.41 % -------------------------------------------------
% 0.13/0.41 % User time : 0.002 s
% 0.13/0.41 % System time : 0.002 s
% 0.13/0.41 % Total time : 0.004 s
% 0.13/0.41 % Maximum resident set size: 3640 pages
% 0.13/0.41
% 0.13/0.41 % -------------------------------------------------
% 0.13/0.41 % User time : 0.011 s
% 0.13/0.41 % System time : 0.011 s
% 0.13/0.41 % Total time : 0.022 s
% 0.13/0.41 % Maximum resident set size: 4864 pages
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------