%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM024-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 0.15s 10.46s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 13 unt; 0 nHn; 22 RR)
% Number of literals : 46 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity,axiom,
( ~ equalish(X2,X3)
| ~ equalish(X1,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
cnf(adding_zero,axiom,
equalish(add(X1,n0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-0.ax',adding_zero) ).
cnf(symmetry,axiom,
( ~ equalish(X1,X2)
| equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
cnf(commutativity_of_plus,axiom,
equalish(add(X1,X2),add(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_plus) ).
cnf(plus_substitution,axiom,
( ~ equalish(add(X1,X2),add(X3,X2))
| equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_substitution) ).
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(prove_a_contradiction,negated_conjecture,
~ equalish(successor(X1),n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_contradiction) ).
cnf(impossible_a_is_less_than_itself,hypothesis,
less(a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',impossible_a_is_less_than_itself) ).
cnf(c_0_8,plain,
( ~ equalish(X2,X3)
| ~ equalish(X1,X2)
| equalish(X1,X3) ),
inference(fof_simplification,[status(thm)],[transitivity]) ).
cnf(c_0_9,plain,
( ~ equalish(X2,X3)
| ~ equalish(X1,X2)
| equalish(X1,X3) ),
c_0_8 ).
cnf(c_0_10,axiom,
equalish(add(X1,n0),X1),
adding_zero ).
cnf(c_0_11,plain,
( ~ equalish(X1,X2)
| equalish(X2,X1) ),
inference(fof_simplification,[status(thm)],[symmetry]) ).
cnf(c_0_12,plain,
( ~ equalish(X1,add(X2,n0))
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,axiom,
equalish(add(X1,X2),add(X2,X1)),
commutativity_of_plus ).
cnf(c_0_14,plain,
( ~ equalish(X1,X2)
| equalish(X2,X1) ),
c_0_11 ).
cnf(c_0_15,plain,
equalish(add(n0,X1),X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
( ~ equalish(add(X1,X2),add(X3,X2))
| equalish(X1,X3) ),
inference(fof_simplification,[status(thm)],[plus_substitution]) ).
cnf(c_0_17,plain,
equalish(X1,add(n0,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( ~ equalish(add(X1,X2),add(X3,X2))
| equalish(X1,X3) ),
c_0_16 ).
cnf(c_0_19,plain,
( ~ equalish(X1,X2)
| equalish(X1,add(n0,X2)) ),
inference(spm,[status(thm)],[c_0_9,c_0_17]) ).
cnf(c_0_20,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_21,negated_conjecture,
~ equalish(successor(X1),n0),
inference(fof_simplification,[status(thm)],[prove_a_contradiction]) ).
cnf(c_0_22,plain,
( ~ equalish(add(X1,X2),X2)
| equalish(X1,n0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ~ less(X1,X2)
| equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2) ),
c_0_20 ).
cnf(c_0_24,negated_conjecture,
~ equalish(successor(X1),n0),
c_0_21 ).
cnf(c_0_25,hypothesis,
less(a,a),
impossible_a_is_less_than_itself ).
cnf(c_0_26,plain,
~ less(X1,X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_27,hypothesis,
$false,
inference(sr,[status(thm)],[c_0_25,c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM024-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/10.39 % Computer : n010.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Mon Sep 21 01:59:40 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/10.43 Running first-order theorem proving
% 0.15/10.43 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
% 0.15/10.46 % Version: 3.5.1
% 0.15/10.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/10.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/10.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/10.46 % Starting new_bool_3 with 300s (1) cores
% 0.15/10.46 % Starting new_bool_1 with 300s (1) cores
% 0.15/10.46 % Starting sh5l with 300s (1) cores
% 0.15/10.46 % sh5l with pid 4007737 completed with status 0
% 0.15/10.46 % Result found by sh5l
% 0.15/10.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/10.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/10.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/10.46 % Starting new_bool_3 with 300s (1) cores
% 0.15/10.46 % Starting new_bool_1 with 300s (1) cores
% 0.15/10.46 % Starting sh5l with 300s (1) cores
% 0.15/10.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.15/10.46 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.15/10.46 % Search class: FHUNM-FFSF21-MFFFFFNN
% 0.15/10.46 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.15/10.46 % Starting SubtermCWHack with 28s (1) cores
% 0.15/10.46 % SubtermCWHack with pid 4007744 completed with status 0
% 0.15/10.46 % Result found by SubtermCWHack
% 0.15/10.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/10.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/10.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/10.46 % Starting new_bool_3 with 300s (1) cores
% 0.15/10.46 % Starting new_bool_1 with 300s (1) cores
% 0.15/10.46 % Starting sh5l with 300s (1) cores
% 0.15/10.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.15/10.46 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.15/10.46 % Search class: FHUNM-FFSF21-MFFFFFNN
% 0.15/10.46 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.15/10.46 % Starting SubtermCWHack with 28s (1) cores
% 0.15/10.46 % Preprocessing time : 0.001 s
% 0.15/10.46
% 0.15/10.46 % Proof found!
% 0.15/10.46 % SZS status Unsatisfiable
% 0.15/10.46 % SZS output start CNFRefutation
% See solution above
% 0.15/10.46 % Parsed axioms : 16
% 0.15/10.46 % Removed by relevancy pruning/SinE : 0
% 0.15/10.46 % Initial clauses : 16
% 0.15/10.46 % Removed in clause preprocessing : 0
% 0.15/10.46 % Initial clauses in saturation : 16
% 0.15/10.46 % Processed clauses : 78
% 0.15/10.46 % ...of these trivial : 3
% 0.15/10.46 % ...subsumed : 8
% 0.15/10.46 % ...remaining for further processing : 67
% 0.15/10.46 % Other redundant clauses eliminated : 0
% 0.15/10.46 % Clauses deleted for lack of memory : 0
% 0.15/10.46 % Backward-subsumed : 0
% 0.15/10.46 % Backward-rewritten : 1
% 0.15/10.46 % Generated clauses : 270
% 0.15/10.46 % ...of the previous two non-redundant : 174
% 0.15/10.46 % ...aggressively subsumed : 0
% 0.15/10.46 % Contextual simplify-reflections : 0
% 0.15/10.46 % Paramodulations : 269
% 0.15/10.46 % Factorizations : 0
% 0.15/10.46 % NegExts : 0
% 0.15/10.46 % Equation resolutions : 0
% 0.15/10.46 % Disequality decompositions : 0
% 0.15/10.46 % Total rewrite steps : 90
% 0.15/10.46 % ...of those cached : 56
% 0.15/10.46 % Propositional unsat checks : 0
% 0.15/10.46 % Propositional check models : 0
% 0.15/10.46 % Propositional check unsatisfiable : 0
% 0.15/10.46 % Propositional clauses : 0
% 0.15/10.46 % Propositional clauses after purity: 0
% 0.15/10.46 % Propositional unsat core size : 0
% 0.15/10.46 % Propositional preprocessing time : 0.000
% 0.15/10.46 % Propositional encoding time : 0.000
% 0.15/10.46 % Propositional solver time : 0.000
% 0.15/10.46 % Success case prop preproc time : 0.000
% 0.15/10.46 % Success case prop encoding time : 0.000
% 0.15/10.46 % Success case prop solver time : 0.000
% 0.15/10.46 % Current number of processed clauses : 65
% 0.15/10.46 % Positive orientable unit clauses : 39
% 0.15/10.46 % Positive unorientable unit clauses: 0
% 0.15/10.46 % Negative unit clauses : 2
% 0.15/10.46 % Non-unit-clauses : 24
% 0.15/10.46 % Current number of unprocessed clauses: 112
% 0.15/10.46 % ...number of literals in the above : 197
% 0.15/10.46 % Current number of archived formulas : 0
% 0.15/10.46 % Current number of archived clauses : 2
% 0.15/10.46 % Clause-clause subsumption calls (NU) : 72
% 0.15/10.46 % Rec. Clause-clause subsumption calls : 72
% 0.15/10.46 % Non-unit clause-clause subsumptions : 8
% 0.15/10.46 % Unit Clause-clause subsumption calls : 3
% 0.15/10.46 % Rewrite failures with RHS unbound : 0
% 0.15/10.46 % BW rewrite match attempts : 11
% 0.15/10.46 % BW rewrite match successes : 1
% 0.15/10.46 % Condensation attempts : 0
% 0.15/10.46 % Condensation successes : 0
% 0.15/10.46 % Termbank termtop insertions : 3081
% 0.15/10.46 % Search garbage collected termcells : 24
% 0.15/10.46
% 0.15/10.46 % -------------------------------------------------
% 0.15/10.46 % User time : 0.008 s
% 0.15/10.46 % System time : 0.001 s
% 0.15/10.46 % Total time : 0.009 s
% 0.15/10.46 % Maximum resident set size: 3600 pages
% 0.15/10.46
% 0.15/10.46 % -------------------------------------------------
% 0.15/10.46 % User time : 0.011 s
% 0.15/10.46 % System time : 0.005 s
% 0.15/10.46 % Total time : 0.015 s
% 0.15/10.46 % Maximum resident set size: 4864 pages
% 0.15/10.46 % E exiting
%------------------------------------------------------------------------------