%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 0.12s 0.47s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 9 RR)
% Number of literals : 24 ( 23 equ; 5 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(goal,negated_conjecture,
'+'(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(sum_s,axiom,
sum(s(X1)) = '+'(s(X1),sum(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_s) ).
cnf(plus_comm,axiom,
'+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_comm) ).
cnf(times_s,axiom,
times(s(X1),X2) = '+'(X2,times(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_s) ).
cnf(plus_assoc,axiom,
'+'(X1,'+'(X2,X3)) = '+'('+'(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_assoc) ).
cnf(times_one,axiom,
times(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_one) ).
cnf(distr,axiom,
times(X1,'+'(X2,X3)) = '+'(times(X1,X2),times(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distr) ).
cnf(induction_hypothesis,axiom,
'+'(sum(a),sum(a)) = times(a,s(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction_hypothesis) ).
cnf(c_0_8,negated_conjecture,
'+'(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))),
inference(fof_simplification,[status(thm)],[goal]) ).
cnf(c_0_9,axiom,
sum(s(X1)) = '+'(s(X1),sum(X1)),
sum_s ).
cnf(c_0_10,axiom,
'+'(X1,X2) = '+'(X2,X1),
plus_comm ).
cnf(c_0_11,negated_conjecture,
'+'(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))),
c_0_8 ).
cnf(c_0_12,plain,
sum(s(X1)) = '+'(sum(X1),s(X1)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,axiom,
times(s(X1),X2) = '+'(X2,times(X1,X2)),
times_s ).
cnf(c_0_14,axiom,
'+'(X1,'+'(X2,X3)) = '+'('+'(X1,X2),X3),
plus_assoc ).
cnf(c_0_15,axiom,
times(X1,one) = X1,
times_one ).
cnf(c_0_16,negated_conjecture,
'+'(s(s(a)),times(a,s(s(a)))) != '+'(sum(a),'+'(s(a),'+'(sum(a),s(a)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_12]),c_0_13]),c_0_14]) ).
cnf(c_0_17,plain,
s(X1) = '+'(one,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_15]) ).
cnf(c_0_18,axiom,
times(X1,'+'(X2,X3)) = '+'(times(X1,X2),times(X1,X3)),
distr ).
cnf(c_0_19,axiom,
'+'(sum(a),sum(a)) = times(a,s(a)),
induction_hypothesis ).
cnf(c_0_20,negated_conjecture,
'+'(sum(a),'+'(one,'+'(a,'+'(one,'+'(a,sum(a)))))) != '+'(one,'+'(one,'+'(a,'+'(a,'+'(a,times(a,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)],[c_0_16,c_0_17]),c_0_17]),c_0_17]),c_0_17]),c_0_18]),c_0_15]),c_0_18]),c_0_15]),c_0_14]),c_0_14]),c_0_17]),c_0_17]),c_0_10]),c_0_14]),c_0_14]) ).
cnf(c_0_21,plain,
'+'(X1,'+'(X2,X3)) = '+'(X2,'+'(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_14]) ).
cnf(c_0_22,plain,
'+'(sum(a),sum(a)) = '+'(a,times(a,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_17]),c_0_18]),c_0_15]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[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_20,c_0_21]),c_0_21]),c_0_21]),c_0_21]),c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 03:28:55 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.12/0.47 % Version: 3.5.1
% 0.12/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.47 % Starting sh5l with 300s (1) cores
% 0.12/0.47 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 870031 completed with status 0
% 0.12/0.47 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.47 % No SInE strategy applied
% 0.12/0.47 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.12/0.47 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.47 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 0.12/0.47 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 0.12/0.47 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 0.12/0.47 % U----_043_B31_F1_PI_AE_CS_SP_S2S with pid 870041 completed with status 0
% 0.12/0.47 % Result found by U----_043_B31_F1_PI_AE_CS_SP_S2S
% 0.12/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.47 % No SInE strategy applied
% 0.12/0.47 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.12/0.47 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.47 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 0.12/0.47 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 0.12/0.47 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 0.12/0.47 % Preprocessing time : 0.001 s
% 0.12/0.47
% 0.12/0.47 % Proof found!
% 0.12/0.47 % SZS status Unsatisfiable
% 0.12/0.47 % SZS output start CNFRefutation
% See solution above
% 0.12/0.47 % Parsed axioms : 15
% 0.12/0.47 % Removed by relevancy pruning/SinE : 0
% 0.12/0.47 % Initial clauses : 15
% 0.12/0.47 % Removed in clause preprocessing : 0
% 0.12/0.47 % Initial clauses in saturation : 15
% 0.12/0.47 % Processed clauses : 44
% 0.12/0.47 % ...of these trivial : 8
% 0.12/0.47 % ...subsumed : 7
% 0.12/0.47 % ...remaining for further processing : 28
% 0.12/0.47 % Other redundant clauses eliminated : 0
% 0.12/0.47 % Clauses deleted for lack of memory : 0
% 0.12/0.47 % Backward-subsumed : 0
% 0.12/0.47 % Backward-rewritten : 7
% 0.12/0.47 % Generated clauses : 177
% 0.12/0.47 % ...of the previous two non-redundant : 137
% 0.12/0.47 % ...aggressively subsumed : 0
% 0.12/0.47 % Contextual simplify-reflections : 0
% 0.12/0.47 % Paramodulations : 177
% 0.12/0.47 % Factorizations : 0
% 0.12/0.47 % NegExts : 0
% 0.12/0.47 % Equation resolutions : 0
% 0.12/0.47 % Disequality decompositions : 0
% 0.12/0.47 % Total rewrite steps : 243
% 0.12/0.47 % ...of those cached : 114
% 0.12/0.47 % Propositional unsat checks : 0
% 0.12/0.47 % Propositional check models : 0
% 0.12/0.47 % Propositional check unsatisfiable : 0
% 0.12/0.47 % Propositional clauses : 0
% 0.12/0.47 % Propositional clauses after purity: 0
% 0.12/0.47 % Propositional unsat core size : 0
% 0.12/0.47 % Propositional preprocessing time : 0.000
% 0.12/0.47 % Propositional encoding time : 0.000
% 0.12/0.47 % Propositional solver time : 0.000
% 0.12/0.47 % Success case prop preproc time : 0.000
% 0.12/0.47 % Success case prop encoding time : 0.000
% 0.12/0.47 % Success case prop solver time : 0.000
% 0.12/0.47 % Current number of processed clauses : 21
% 0.12/0.47 % Positive orientable unit clauses : 17
% 0.12/0.47 % Positive unorientable unit clauses: 4
% 0.12/0.47 % Negative unit clauses : 0
% 0.12/0.47 % Non-unit-clauses : 0
% 0.12/0.47 % Current number of unprocessed clauses: 101
% 0.12/0.47 % ...number of literals in the above : 101
% 0.12/0.47 % Current number of archived formulas : 0
% 0.12/0.47 % Current number of archived clauses : 7
% 0.12/0.47 % Clause-clause subsumption calls (NU) : 0
% 0.12/0.47 % Rec. Clause-clause subsumption calls : 0
% 0.12/0.47 % Non-unit clause-clause subsumptions : 0
% 0.12/0.47 % Unit Clause-clause subsumption calls : 3
% 0.12/0.47 % Rewrite failures with RHS unbound : 0
% 0.12/0.47 % BW rewrite match attempts : 39
% 0.12/0.47 % BW rewrite match successes : 39
% 0.12/0.47 % Condensation attempts : 0
% 0.12/0.47 % Condensation successes : 0
% 0.12/0.47 % Termbank termtop insertions : 1983
% 0.12/0.47 % Search garbage collected termcells : 2
% 0.12/0.47
% 0.12/0.47 % -------------------------------------------------
% 0.12/0.47 % User time : 0.005 s
% 0.12/0.47 % System time : 0.004 s
% 0.12/0.47 % Total time : 0.010 s
% 0.12/0.47 % Maximum resident set size: 3636 pages
% 0.12/0.47
% 0.12/0.47 % -------------------------------------------------
% 0.12/0.47 % User time : 0.031 s
% 0.12/0.47 % System time : 0.016 s
% 0.12/0.47 % Total time : 0.048 s
% 0.12/0.47 % Maximum resident set size: 4608 pages
% 0.12/0.47 % E exiting
%------------------------------------------------------------------------------