%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN133-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 01:57:46 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.43s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of clauses : 38 ( 38 unt; 0 nHn; 9 RR)
% Number of literals : 38 ( 37 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(goal,negated_conjecture,
times(sum(s(a)),sum(s(a))) != cubes(s(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(sum_s,axiom,
sum(s(X1)) = '+'(s(X1),sum(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_s) ).
cnf(plus_comm,axiom,
'+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_comm) ).
cnf(cubes_s,axiom,
cubes(s(X1)) = '+'(times(s(X1),times(s(X1),s(X1))),cubes(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cubes_s) ).
cnf(times_s,axiom,
times(s(X1),X2) = '+'(X2,times(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_s) ).
cnf(plus_sum,axiom,
'+'(sum(X1),sum(X1)) = times(X1,s(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_sum) ).
cnf(induction_hypothesis,axiom,
times(sum(a),sum(a)) = cubes(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction_hypothesis) ).
cnf(plus_assoc,axiom,
'+'(X1,'+'(X2,X3)) = '+'('+'(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_assoc) ).
cnf(distr,axiom,
times(X1,'+'(X2,X3)) = '+'(times(X1,X2),times(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distr) ).
cnf(distr_001,axiom,
times('+'(X1,X2),X3) = '+'(times(X1,X3),times(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distr_001) ).
cnf(times_one,axiom,
times(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_one) ).
cnf(times_comm,axiom,
times(X1,X2) = times(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_comm) ).
cnf(times_assoc,axiom,
times(X1,times(X2,X3)) = times(times(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_assoc) ).
cnf(c_0_13,negated_conjecture,
times(sum(s(a)),sum(s(a))) != cubes(s(a)),
inference(fof_simplification,[status(thm)],[goal]) ).
cnf(c_0_14,axiom,
sum(s(X1)) = '+'(s(X1),sum(X1)),
sum_s ).
cnf(c_0_15,axiom,
'+'(X1,X2) = '+'(X2,X1),
plus_comm ).
cnf(c_0_16,negated_conjecture,
times(sum(s(a)),sum(s(a))) != cubes(s(a)),
c_0_13 ).
cnf(c_0_17,plain,
sum(s(X1)) = '+'(sum(X1),s(X1)),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
cubes(s(X1)) = '+'(times(s(X1),times(s(X1),s(X1))),cubes(X1)),
cubes_s ).
cnf(c_0_19,axiom,
times(s(X1),X2) = '+'(X2,times(X1,X2)),
times_s ).
cnf(c_0_20,axiom,
'+'(sum(X1),sum(X1)) = times(X1,s(X1)),
plus_sum ).
cnf(c_0_21,negated_conjecture,
cubes(s(a)) != times('+'(sum(a),s(a)),'+'(sum(a),s(a))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]) ).
cnf(c_0_22,plain,
cubes(s(X1)) = '+'(cubes(X1),'+'('+'('+'(sum(X1),sum(X1)),s(X1)),times(X1,'+'('+'(sum(X1),sum(X1)),s(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_15]),c_0_19]),c_0_15]) ).
cnf(c_0_23,axiom,
times(sum(a),sum(a)) = cubes(a),
induction_hypothesis ).
cnf(c_0_24,negated_conjecture,
times('+'(sum(a),s(a)),'+'(sum(a),s(a))) != '+'(times(sum(a),sum(a)),'+'('+'('+'(sum(a),sum(a)),s(a)),times(a,'+'('+'(sum(a),sum(a)),s(a))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_25,axiom,
'+'(X1,'+'(X2,X3)) = '+'('+'(X1,X2),X3),
plus_assoc ).
cnf(c_0_26,axiom,
times(X1,'+'(X2,X3)) = '+'(times(X1,X2),times(X1,X3)),
distr ).
cnf(c_0_27,axiom,
times('+'(X1,X2),X3) = '+'(times(X1,X3),times(X2,X3)),
distr_001 ).
cnf(c_0_28,axiom,
times(X1,one) = X1,
times_one ).
cnf(c_0_29,axiom,
times(X1,X2) = times(X2,X1),
times_comm ).
cnf(c_0_30,axiom,
times(X1,times(X2,X3)) = times(times(X1,X2),X3),
times_assoc ).
cnf(c_0_31,negated_conjecture,
'+'(sum(a),'+'(times(a,sum(a)),'+'(times(sum(a),sum(a)),'+'(sum(a),'+'(sum(a),'+'(s(a),times(sum(a),s(a)))))))) != '+'(times(sum(a),sum(a)),'+'(sum(a),'+'(sum(a),'+'(times(a,sum(a)),'+'(sum(a),'+'(sum(a),'+'(times(a,sum(a)),s(a)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_25]),c_0_25]),c_0_26]),c_0_27]),c_0_19]),c_0_15]),c_0_25]),c_0_27]),c_0_19]),c_0_20]),c_0_15]),c_0_25]),c_0_15]),c_0_25]),c_0_25]),c_0_25]),c_0_25]),c_0_26]),c_0_26]),c_0_20]),c_0_15]),c_0_25]),c_0_15]),c_0_25]),c_0_25]),c_0_25]) ).
cnf(c_0_32,plain,
s(X1) = '+'(one,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_19]),c_0_28]) ).
cnf(c_0_33,plain,
'+'(X1,X2) = '+'(X2,X1),
c_0_15 ).
cnf(c_0_34,plain,
times(X1,X2) = times(X2,X1),
c_0_29 ).
cnf(c_0_35,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
c_0_25 ).
cnf(c_0_36,plain,
times(times(X1,X2),X3) = times(X1,times(X2,X3)),
c_0_30 ).
cnf(c_0_37,negated_conjecture,
$false,
inference(ar,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]),c_0_26]),c_0_28]),c_0_29]),c_0_25]),c_0_15]),c_0_25]),c_0_25]),c_0_25]),c_0_25]),c_0_25]),c_0_32]),c_0_15]),c_0_25]),c_0_15]),c_0_25]),c_0_25]),c_0_25]),c_0_25]),c_0_25]),c_0_25]),c_0_25]),c_0_33,c_0_34,c_0_35,c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN133-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n020.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 : Mon Sep 21 03:29:47 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.43 % Version: 3.5.1
% 0.15/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.43 % Starting sh5l with 300s (1) cores
% 0.15/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1904957 completed with status 0
% 0.15/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.43 % No SInE strategy applied
% 0.15/0.43 % Search class: FUUPM-FFSS21-MFFFFFNN
% 0.15/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.43 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with 136s (1) cores
% 0.15/0.43 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 136s (1) cores
% 0.15/0.43 % Starting G-E--_209_C18_F1_AE_CS_SP_S0Y with 136s (1) cores
% 0.15/0.43 % G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with pid 1904966 completed with status 0
% 0.15/0.43 % Result found by G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN
% 0.15/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.43 % No SInE strategy applied
% 0.15/0.43 % Search class: FUUPM-FFSS21-MFFFFFNN
% 0.15/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.43 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with 136s (1) cores
% 0.15/0.43 % Preprocessing time : 0.001 s
% 0.15/0.43 % Presaturation interreduction done
% 0.15/0.43
% 0.15/0.43 % Proof found!
% 0.15/0.43 % SZS status Unsatisfiable
% 0.15/0.43 % SZS output start CNFRefutation
% See solution above
% 0.15/0.43 % Parsed axioms : 18
% 0.15/0.43 % Removed by relevancy pruning/SinE : 0
% 0.15/0.43 % Initial clauses : 18
% 0.15/0.43 % Removed in clause preprocessing : 0
% 0.15/0.43 % Initial clauses in saturation : 18
% 0.15/0.43 % Processed clauses : 44
% 0.15/0.43 % ...of these trivial : 2
% 0.15/0.43 % ...subsumed : 0
% 0.15/0.43 % ...remaining for further processing : 41
% 0.15/0.43 % Other redundant clauses eliminated : 0
% 0.15/0.43 % Clauses deleted for lack of memory : 0
% 0.15/0.43 % Backward-subsumed : 0
% 0.15/0.43 % Backward-rewritten : 8
% 0.15/0.43 % Generated clauses : 64
% 0.15/0.43 % ...of the previous two non-redundant : 46
% 0.15/0.43 % ...aggressively subsumed : 0
% 0.15/0.43 % Contextual simplify-reflections : 0
% 0.15/0.43 % Paramodulations : 64
% 0.15/0.43 % Factorizations : 0
% 0.15/0.43 % NegExts : 0
% 0.15/0.43 % Equation resolutions : 0
% 0.15/0.43 % Disequality decompositions : 0
% 0.15/0.43 % Total rewrite steps : 161
% 0.15/0.43 % ...of those cached : 45
% 0.15/0.43 % Propositional unsat checks : 0
% 0.15/0.43 % Propositional check models : 0
% 0.15/0.43 % Propositional check unsatisfiable : 0
% 0.15/0.43 % Propositional clauses : 0
% 0.15/0.43 % Propositional clauses after purity: 0
% 0.15/0.43 % Propositional unsat core size : 0
% 0.15/0.43 % Propositional preprocessing time : 0.000
% 0.15/0.43 % Propositional encoding time : 0.000
% 0.15/0.43 % Propositional solver time : 0.000
% 0.15/0.43 % Success case prop preproc time : 0.000
% 0.15/0.43 % Success case prop encoding time : 0.000
% 0.15/0.43 % Success case prop solver time : 0.000
% 0.15/0.43 % Current number of processed clauses : 15
% 0.15/0.43 % Positive orientable unit clauses : 13
% 0.15/0.43 % Positive unorientable unit clauses: 2
% 0.15/0.43 % Negative unit clauses : 0
% 0.15/0.43 % Non-unit-clauses : 0
% 0.15/0.43 % Current number of unprocessed clauses: 38
% 0.15/0.43 % ...number of literals in the above : 38
% 0.15/0.43 % Current number of archived formulas : 0
% 0.15/0.43 % Current number of archived clauses : 26
% 0.15/0.43 % Clause-clause subsumption calls (NU) : 0
% 0.15/0.43 % Rec. Clause-clause subsumption calls : 0
% 0.15/0.43 % Non-unit clause-clause subsumptions : 0
% 0.15/0.43 % Unit Clause-clause subsumption calls : 0
% 0.15/0.43 % Rewrite failures with RHS unbound : 0
% 0.15/0.43 % BW rewrite match attempts : 26
% 0.15/0.43 % BW rewrite match successes : 26
% 0.15/0.43 % Condensation attempts : 0
% 0.15/0.43 % Condensation successes : 0
% 0.15/0.43 % Termbank termtop insertions : 1176
% 0.15/0.43 % Search garbage collected termcells : 2
% 0.15/0.43
% 0.15/0.43 % -------------------------------------------------
% 0.15/0.43 % User time : 0.007 s
% 0.15/0.43 % System time : 0.002 s
% 0.15/0.43 % Total time : 0.009 s
% 0.15/0.43 % Maximum resident set size: 3640 pages
% 0.15/0.43
% 0.15/0.43 % -------------------------------------------------
% 0.15/0.43 % User time : 0.031 s
% 0.15/0.43 % System time : 0.011 s
% 0.15/0.43 % Total time : 0.043 s
% 0.15/0.43 % Maximum resident set size: 4608 pages
% 0.15/0.43 % E exiting
%------------------------------------------------------------------------------