%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LDA002-1 : 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 : n015.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 01:24:45 PM UTC 2026
% Result : Unsatisfiable 0.45s 0.48s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 68 ( 68 unt; 0 nHn; 52 RR)
% Number of literals : 68 ( 67 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a1,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),f(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
cnf(clause_2,axiom,
n2 = f(n1,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
cnf(clause_7,axiom,
u3 = f(u,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
cnf(clause_4,axiom,
u = f(n2,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
cnf(clause_6,axiom,
u2 = f(u,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
cnf(clause_5,axiom,
u1 = f(u,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
cnf(clause_10,axiom,
b = f(u1,u3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10) ).
cnf(clause_3,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
cnf(clause_8,axiom,
uu = f(u,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
cnf(clause_11,axiom,
v = f(uu,uu),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11) ).
cnf(clause_9,axiom,
a = f(f(n3,n2),u2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
cnf(prove_equation,negated_conjecture,
f(a,v) != f(b,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
cnf(c_0_12,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),f(X1,X3)),
a1 ).
cnf(c_0_13,axiom,
n2 = f(n1,n1),
clause_2 ).
cnf(c_0_14,axiom,
u3 = f(u,n3),
clause_7 ).
cnf(c_0_15,plain,
f(f(n1,X1),n2) = f(n1,f(X1,n1)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
u = f(n2,n2),
clause_4 ).
cnf(c_0_17,axiom,
u2 = f(u,n2),
clause_6 ).
cnf(c_0_18,plain,
f(f(u,X1),u3) = f(u,f(X1,n3)),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_19,axiom,
u1 = f(u,n1),
clause_5 ).
cnf(c_0_20,axiom,
b = f(u1,u3),
clause_10 ).
cnf(c_0_21,plain,
f(n1,n2) = u,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_16]),c_0_13]) ).
cnf(c_0_22,axiom,
n3 = f(n2,n1),
clause_3 ).
cnf(c_0_23,plain,
f(f(u,X1),u2) = f(u,f(X1,n2)),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_24,axiom,
uu = f(u,u),
clause_8 ).
cnf(c_0_25,plain,
f(u,f(n1,n3)) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_26,plain,
f(n1,n3) = u2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_21]),c_0_17]),c_0_22]) ).
cnf(c_0_27,axiom,
v = f(uu,uu),
clause_11 ).
cnf(c_0_28,plain,
f(uu,u2) = f(u,u2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_17]) ).
cnf(c_0_29,plain,
f(u,u2) = b,
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
f(f(u,X1),uu) = f(u,f(X1,u)),
inference(spm,[status(thm)],[c_0_12,c_0_24]) ).
cnf(c_0_31,plain,
f(f(n2,X1),u) = f(n2,f(X1,n2)),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_32,plain,
f(f(uu,X1),v) = f(uu,f(X1,uu)),
inference(spm,[status(thm)],[c_0_12,c_0_27]) ).
cnf(c_0_33,plain,
f(uu,u2) = b,
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
f(u,f(n2,u)) = f(u2,uu),
inference(spm,[status(thm)],[c_0_30,c_0_17]) ).
cnf(c_0_35,plain,
f(n2,u) = uu,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_16]),c_0_24]),c_0_16]) ).
cnf(c_0_36,plain,
f(u,uu) = v,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_24]),c_0_27]),c_0_24]) ).
cnf(c_0_37,axiom,
a = f(f(n3,n2),u2),
clause_9 ).
cnf(c_0_38,plain,
f(n1,f(n1,X1)) = f(n2,f(n1,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_39,negated_conjecture,
f(a,v) != f(b,v),
inference(fof_simplification,[status(thm)],[prove_equation]) ).
cnf(c_0_40,plain,
f(uu,f(u2,uu)) = f(b,v),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,plain,
f(u2,uu) = v,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_42,plain,
f(f(f(n3,n2),X1),a) = f(f(n3,n2),f(X1,u2)),
inference(spm,[status(thm)],[c_0_12,c_0_37]) ).
cnf(c_0_43,plain,
f(u2,u2) = uu,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_17]),c_0_16]),c_0_24]) ).
cnf(c_0_44,plain,
f(n3,u) = uu,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_22]),c_0_21]),c_0_35]) ).
cnf(c_0_45,plain,
f(n3,f(n2,X1)) = f(n2,f(n1,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_22]) ).
cnf(c_0_46,plain,
f(n1,u) = uu,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_21]),c_0_35]) ).
cnf(c_0_47,plain,
f(u,f(n2,X1)) = f(n2,f(n2,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_48,negated_conjecture,
f(a,v) != f(b,v),
c_0_39 ).
cnf(c_0_49,plain,
f(b,v) = f(uu,v),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,plain,
f(uu,f(u,X1)) = f(u,f(u,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_24]) ).
cnf(c_0_51,plain,
f(f(n3,n2),uu) = f(a,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_37]),c_0_43]) ).
cnf(c_0_52,plain,
f(f(n3,X1),uu) = f(n3,f(X1,u)),
inference(spm,[status(thm)],[c_0_12,c_0_44]) ).
cnf(c_0_53,plain,
f(n3,uu) = f(n2,uu),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_35]),c_0_46]) ).
cnf(c_0_54,plain,
f(n2,uu) = v,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_35]),c_0_36]) ).
cnf(c_0_55,negated_conjecture,
f(a,v) != f(uu,v),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,plain,
f(uu,v) = f(u,v),
inference(spm,[status(thm)],[c_0_50,c_0_36]) ).
cnf(c_0_57,plain,
f(f(n3,n2),f(u2,X1)) = f(a,f(f(n3,n2),X1)),
inference(spm,[status(thm)],[c_0_12,c_0_37]) ).
cnf(c_0_58,plain,
f(a,a) = v,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_35]),c_0_53]),c_0_54]) ).
cnf(c_0_59,plain,
f(n3,uu) = v,
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,plain,
f(n1,uu) = f(n2,uu),
inference(spm,[status(thm)],[c_0_38,c_0_46]) ).
cnf(c_0_61,negated_conjecture,
f(a,v) != f(u,v),
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,plain,
f(u,v) = f(n2,v),
inference(spm,[status(thm)],[c_0_47,c_0_54]) ).
cnf(c_0_63,plain,
f(f(n3,n2),v) = f(a,v),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_41]),c_0_51]),c_0_58]) ).
cnf(c_0_64,plain,
f(f(n3,X1),v) = f(n3,f(X1,uu)),
inference(spm,[status(thm)],[c_0_12,c_0_59]) ).
cnf(c_0_65,plain,
f(n3,v) = f(n2,v),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_54]),c_0_60]),c_0_54]) ).
cnf(c_0_66,negated_conjecture,
f(a,v) != f(n2,v),
inference(rw,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64]),c_0_54]),c_0_65]),c_0_66]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LDA002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 01:19:51 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.42 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
% 0.45/0.48 % Version: 3.5.1
% 0.45/0.48 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.45/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.48 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.45/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.45/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.45/0.48 % Starting sh5l with 300s (1) cores
% 0.45/0.48 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 244710 completed with status 0
% 0.45/0.48 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.45/0.48 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.45/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.48 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.45/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.45/0.48 % No SInE strategy applied
% 0.45/0.48 % Search class: FUUPF-FFSM22-SFFFFFNN
% 0.45/0.48 % partial match(1): FUUPF-FFSF22-SFFFFFNN
% 0.45/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.45/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.45/0.48 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.45/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.45/0.48 % Starting new_bool_3 with 136s (1) cores
% 0.45/0.48 % Starting new_bool_1 with 136s (1) cores
% 0.45/0.48 % SubtermCWHack with pid 244714 completed with status 0
% 0.45/0.48 % Result found by SubtermCWHack
% 0.45/0.48 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.45/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.48 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.45/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.45/0.48 % No SInE strategy applied
% 0.45/0.48 % Search class: FUUPF-FFSM22-SFFFFFNN
% 0.45/0.48 % partial match(1): FUUPF-FFSF22-SFFFFFNN
% 0.45/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.45/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.45/0.48 % Preprocessing time : 0.001 s
% 0.45/0.48
% 0.45/0.48 % Proof found!
% 0.45/0.48 % SZS status Unsatisfiable
% 0.45/0.48 % SZS output start CNFRefutation
% See solution above
% 0.45/0.48 % Parsed axioms : 12
% 0.45/0.48 % Removed by relevancy pruning/SinE : 0
% 0.45/0.48 % Initial clauses : 12
% 0.45/0.48 % Removed in clause preprocessing : 0
% 0.45/0.48 % Initial clauses in saturation : 12
% 0.45/0.48 % Processed clauses : 241
% 0.45/0.48 % ...of these trivial : 13
% 0.45/0.48 % ...subsumed : 0
% 0.45/0.48 % ...remaining for further processing : 228
% 0.45/0.48 % Other redundant clauses eliminated : 0
% 0.45/0.48 % Clauses deleted for lack of memory : 0
% 0.45/0.48 % Backward-subsumed : 0
% 0.45/0.48 % Backward-rewritten : 54
% 0.45/0.48 % Generated clauses : 5789
% 0.45/0.48 % ...of the previous two non-redundant : 5201
% 0.45/0.48 % ...aggressively subsumed : 0
% 0.45/0.48 % Contextual simplify-reflections : 0
% 0.45/0.48 % Paramodulations : 5789
% 0.45/0.48 % Factorizations : 0
% 0.45/0.48 % NegExts : 0
% 0.45/0.48 % Equation resolutions : 0
% 0.45/0.48 % Disequality decompositions : 0
% 0.45/0.48 % Total rewrite steps : 4140
% 0.45/0.48 % ...of those cached : 3069
% 0.45/0.48 % Propositional unsat checks : 0
% 0.45/0.48 % Propositional check models : 0
% 0.45/0.48 % Propositional check unsatisfiable : 0
% 0.45/0.48 % Propositional clauses : 0
% 0.45/0.48 % Propositional clauses after purity: 0
% 0.45/0.48 % Propositional unsat core size : 0
% 0.45/0.48 % Propositional preprocessing time : 0.000
% 0.45/0.48 % Propositional encoding time : 0.000
% 0.45/0.48 % Propositional solver time : 0.000
% 0.45/0.48 % Success case prop preproc time : 0.000
% 0.45/0.48 % Success case prop encoding time : 0.000
% 0.45/0.48 % Success case prop solver time : 0.000
% 0.45/0.48 % Current number of processed clauses : 174
% 0.45/0.48 % Positive orientable unit clauses : 173
% 0.45/0.48 % Positive unorientable unit clauses: 0
% 0.45/0.48 % Negative unit clauses : 1
% 0.45/0.48 % Non-unit-clauses : 0
% 0.45/0.48 % Current number of unprocessed clauses: 4933
% 0.45/0.48 % ...number of literals in the above : 4933
% 0.45/0.48 % Current number of archived formulas : 0
% 0.45/0.48 % Current number of archived clauses : 54
% 0.45/0.48 % Clause-clause subsumption calls (NU) : 0
% 0.45/0.48 % Rec. Clause-clause subsumption calls : 0
% 0.45/0.48 % Non-unit clause-clause subsumptions : 0
% 0.45/0.48 % Unit Clause-clause subsumption calls : 0
% 0.45/0.48 % Rewrite failures with RHS unbound : 0
% 0.45/0.48 % BW rewrite match attempts : 43
% 0.45/0.48 % BW rewrite match successes : 41
% 0.45/0.48 % Condensation attempts : 0
% 0.45/0.48 % Condensation successes : 0
% 0.45/0.48 % Termbank termtop insertions : 123980
% 0.45/0.48 % Search garbage collected termcells : 2
% 0.45/0.48
% 0.45/0.48 % -------------------------------------------------
% 0.45/0.48 % User time : 0.041 s
% 0.45/0.48 % System time : 0.006 s
% 0.45/0.48 % Total time : 0.046 s
% 0.45/0.48 % Maximum resident set size: 3632 pages
% 0.45/0.48
% 0.45/0.48 % -------------------------------------------------
% 0.45/0.48 % User time : 0.178 s
% 0.45/0.48 % System time : 0.033 s
% 0.45/0.48 % Total time : 0.211 s
% 0.45/0.48 % Maximum resident set size: 4608 pages
% 0.45/0.48 % E exiting
%------------------------------------------------------------------------------