%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUN135-1.006 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 01:58:02 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 4 RR)
% Number of literals : 36 ( 35 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 76 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(rule13,axiom,
f(s(X1),s(X2),X3,X4) = if('<='(X1,X2),f(s(X1),minus(X2,X1),X3,X4),f(X1,X4,X3,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule13) ).
cnf(rule2,axiom,
minus(s(X1),s(X2)) = minus(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule2) ).
cnf(rule5,axiom,
'<='(s(X1),s(X2)) = '<='(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule5) ).
cnf(rule4,axiom,
'<='(s(X1),zero) = false,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule4) ).
cnf(rule7,axiom,
if(false,X1,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule7) ).
cnf(rule9,axiom,
perfectp(s(X1)) = f(X1,s(zero),s(X1),s(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule9) ).
cnf(rule1,axiom,
minus(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule1) ).
cnf(rule3,axiom,
'<='(zero,X1) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule3) ).
cnf(rule6,axiom,
if(true,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule6) ).
cnf(goal,negated_conjecture,
perfectp(X1) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(rule12,axiom,
f(s(X1),zero,X2,X3) = f(X1,X3,minus(X2,s(X1)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule12) ).
cnf(rule10,axiom,
f(zero,X1,zero,X2) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule10) ).
cnf(c_0_12,axiom,
f(s(X1),s(X2),X3,X4) = if('<='(X1,X2),f(s(X1),minus(X2,X1),X3,X4),f(X1,X4,X3,X4)),
rule13 ).
cnf(c_0_13,axiom,
minus(s(X1),s(X2)) = minus(X1,X2),
rule2 ).
cnf(c_0_14,axiom,
'<='(s(X1),s(X2)) = '<='(X1,X2),
rule5 ).
cnf(c_0_15,plain,
if('<='(X1,X2),f(s(s(X1)),minus(X2,X1),X3,X4),f(s(X1),X4,X3,X4)) = f(s(s(X1)),s(s(X2)),X3,X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_16,axiom,
'<='(s(X1),zero) = false,
rule4 ).
cnf(c_0_17,axiom,
if(false,X1,X2) = X2,
rule7 ).
cnf(c_0_18,plain,
if('<='(X1,X2),f(s(s(s(X1))),minus(X2,X1),X3,X4),f(s(s(X1)),X4,X3,X4)) = f(s(s(s(X1))),s(s(s(X2))),X3,X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_14]) ).
cnf(c_0_19,axiom,
perfectp(s(X1)) = f(X1,s(zero),s(X1),s(X1)),
rule9 ).
cnf(c_0_20,plain,
f(s(s(X1)),s(zero),X2,X3) = f(s(X1),X3,X2,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_16]),c_0_17]) ).
cnf(c_0_21,plain,
if('<='(X1,X2),f(s(s(s(s(X1)))),minus(X2,X1),X3,X4),f(s(s(s(X1))),X4,X3,X4)) = f(s(s(s(s(X1)))),s(s(s(s(X2)))),X3,X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_13]),c_0_14]) ).
cnf(c_0_22,axiom,
minus(X1,zero) = X1,
rule1 ).
cnf(c_0_23,axiom,
'<='(zero,X1) = true,
rule3 ).
cnf(c_0_24,axiom,
if(true,X1,X2) = X1,
rule6 ).
cnf(c_0_25,negated_conjecture,
perfectp(X1) != true,
inference(fof_simplification,[status(thm)],[goal]) ).
cnf(c_0_26,plain,
f(s(X1),s(s(s(X1))),s(s(s(X1))),s(s(s(X1)))) = perfectp(s(s(s(X1)))),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
f(s(s(s(s(zero)))),s(s(s(s(X1)))),X2,X3) = f(s(s(s(s(zero)))),X1,X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24]) ).
cnf(c_0_28,plain,
f(s(s(s(X1))),s(s(zero)),X2,X3) = f(s(s(X1)),X3,X2,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_29,plain,
f(s(s(s(zero))),s(s(s(X1))),X2,X3) = f(s(s(s(zero))),X1,X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_22]),c_0_23]),c_0_24]) ).
cnf(c_0_30,axiom,
f(s(X1),zero,X2,X3) = f(X1,X3,minus(X2,s(X1)),X3),
rule12 ).
cnf(c_0_31,plain,
f(s(s(zero)),s(s(X1)),X2,X3) = f(s(s(zero)),X1,X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_22]),c_0_23]),c_0_24]) ).
cnf(c_0_32,plain,
f(s(zero),s(X1),X2,X3) = f(s(zero),X1,X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_22]),c_0_23]),c_0_24]) ).
cnf(c_0_33,axiom,
f(zero,X1,zero,X2) = true,
rule10 ).
cnf(c_0_34,negated_conjecture,
perfectp(X1) != true,
c_0_25 ).
cnf(c_0_35,plain,
$false,
inference(sr,[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(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29]),c_0_29]),c_0_30]),c_0_13]),c_0_13]),c_0_13]),c_0_22]),c_0_31]),c_0_31]),c_0_31]),c_0_30]),c_0_13]),c_0_13]),c_0_22]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_30]),c_0_13]),c_0_22]),c_0_33]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN135-1.006 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n012.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 03:28:36 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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 1466671 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: FUUPM-FFSF32-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--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 0.13/0.41 % Starting G-E--_208_B02_F1_AE_CS_SP_PS_S0Y with 136s (1) cores
% 0.13/0.41 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 0.13/0.41 % G-E--_208_B02_F1_AE_CS_SP_PS_S0Y with pid 1466680 completed with status 0
% 0.13/0.41 % Result found by G-E--_208_B02_F1_AE_CS_SP_PS_S0Y
% 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: FUUPM-FFSF32-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--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 0.13/0.41 % Starting G-E--_208_B02_F1_AE_CS_SP_PS_S0Y 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 : 14
% 0.13/0.41 % Removed by relevancy pruning/SinE : 0
% 0.13/0.41 % Initial clauses : 14
% 0.13/0.41 % Removed in clause preprocessing : 0
% 0.13/0.41 % Initial clauses in saturation : 14
% 0.13/0.41 % Processed clauses : 73
% 0.13/0.41 % ...of these trivial : 12
% 0.13/0.41 % ...subsumed : 5
% 0.13/0.41 % ...remaining for further processing : 56
% 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 : 0
% 0.13/0.41 % Generated clauses : 127
% 0.13/0.41 % ...of the previous two non-redundant : 95
% 0.13/0.41 % ...aggressively subsumed : 0
% 0.13/0.41 % Contextual simplify-reflections : 0
% 0.13/0.41 % Paramodulations : 127
% 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 : 282
% 0.13/0.41 % ...of those cached : 131
% 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 : 42
% 0.13/0.41 % Positive orientable unit clauses : 40
% 0.13/0.41 % Positive unorientable unit clauses: 0
% 0.13/0.41 % Negative unit clauses : 2
% 0.13/0.41 % Non-unit-clauses : 0
% 0.13/0.41 % Current number of unprocessed clauses: 46
% 0.13/0.41 % ...number of literals in the above : 46
% 0.13/0.41 % Current number of archived formulas : 0
% 0.13/0.41 % Current number of archived clauses : 14
% 0.13/0.41 % Clause-clause subsumption calls (NU) : 0
% 0.13/0.41 % Rec. Clause-clause subsumption calls : 0
% 0.13/0.41 % Non-unit clause-clause subsumptions : 0
% 0.13/0.41 % Unit Clause-clause subsumption calls : 1
% 0.13/0.41 % Rewrite failures with RHS unbound : 0
% 0.13/0.41 % BW rewrite match attempts : 103
% 0.13/0.41 % BW rewrite match successes : 0
% 0.13/0.41 % Condensation attempts : 0
% 0.13/0.41 % Condensation successes : 0
% 0.13/0.41 % Termbank termtop insertions : 4697
% 0.13/0.41 % Search garbage collected termcells : 2
% 0.13/0.41
% 0.13/0.41 % -------------------------------------------------
% 0.13/0.41 % User time : 0.009 s
% 0.13/0.41 % System time : 0.000 s
% 0.13/0.41 % Total time : 0.009 s
% 0.13/0.41 % Maximum resident set size: 3380 pages
% 0.13/0.41
% 0.13/0.41 % -------------------------------------------------
% 0.13/0.41 % User time : 0.039 s
% 0.13/0.41 % System time : 0.008 s
% 0.13/0.41 % Total time : 0.047 s
% 0.13/0.41 % Maximum resident set size: 4608 pages
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------