%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG440-1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 11:56:06 AM UTC 2026
% Result : Unsatisfiable 0.64s 0.51s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of clauses : 50 ( 32 unt; 0 nHn; 33 RR)
% Number of literals : 87 ( 17 equ; 40 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 143 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos_010,axiom,
( ~ r(X4,X5,X6)
| ~ r(X1,X2,X3)
| r(v(X1,X4),v(X2,X5),v(X3,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_010) ).
cnf(sos_007,axiom,
u(X1,X1,X2) = v(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_007) ).
cnf(sos_009,axiom,
( ~ r(X7,X8,X9)
| ~ r(X4,X5,X6)
| ~ r(X1,X2,X3)
| r(u(X1,X4,X7),u(X2,X5,X8),u(X3,X6,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_009) ).
cnf(sos_006,axiom,
v(X1,X2) = v(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_006) ).
cnf(sos_012,axiom,
r(a,b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_012) ).
cnf(sos_013,axiom,
r(b,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_013) ).
cnf(sos_005,axiom,
u(X1,X1,X2) = u(X2,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_005) ).
cnf(sos_008,axiom,
( ~ r(X7,X8,X9)
| ~ r(X4,X5,X6)
| ~ r(X1,X2,X3)
| r(m(X1,X4,X7),m(X2,X5,X8),m(X3,X6,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_008) ).
cnf(sos_011,axiom,
r(a,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_011) ).
cnf(sos_002,axiom,
u(X1,X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_002) ).
cnf(sos_004,axiom,
u(X1,X1,X2) = u(X1,X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_004) ).
cnf(sos_001,axiom,
m(X1,X2,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_001) ).
cnf(sos,axiom,
m(X1,X1,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos) ).
cnf(goals,negated_conjecture,
~ r(a,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_14,plain,
( ~ r(X4,X5,X6)
| ~ r(X1,X2,X3)
| r(v(X1,X4),v(X2,X5),v(X3,X6)) ),
inference(fof_simplification,[status(thm)],[sos_010]) ).
cnf(c_0_15,plain,
( ~ r(X4,X5,X6)
| ~ r(X1,X2,X3)
| r(v(X1,X4),v(X2,X5),v(X3,X6)) ),
c_0_14 ).
cnf(c_0_16,axiom,
u(X1,X1,X2) = v(X1,X2),
sos_007 ).
cnf(c_0_17,plain,
( ~ r(X7,X8,X9)
| ~ r(X4,X5,X6)
| ~ r(X1,X2,X3)
| r(u(X1,X4,X7),u(X2,X5,X8),u(X3,X6,X9)) ),
inference(fof_simplification,[status(thm)],[sos_009]) ).
cnf(c_0_18,axiom,
v(X1,X2) = v(X2,X1),
sos_006 ).
cnf(c_0_19,plain,
( ~ r(X1,X2,X3)
| ~ r(X4,X5,X6)
| r(u(X1,X1,X4),u(X2,X2,X5),u(X3,X3,X6)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]),c_0_16]) ).
cnf(c_0_20,axiom,
r(a,b,a),
sos_012 ).
cnf(c_0_21,plain,
( ~ r(X7,X8,X9)
| ~ r(X4,X5,X6)
| ~ r(X1,X2,X3)
| r(u(X1,X4,X7),u(X2,X5,X8),u(X3,X6,X9)) ),
c_0_17 ).
cnf(c_0_22,axiom,
r(b,a,a),
sos_013 ).
cnf(c_0_23,plain,
u(X1,X1,X2) = u(X2,X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_16]),c_0_16]) ).
cnf(c_0_24,axiom,
u(X1,X1,X2) = u(X2,X1,X1),
sos_005 ).
cnf(c_0_25,plain,
( ~ r(X7,X8,X9)
| ~ r(X4,X5,X6)
| ~ r(X1,X2,X3)
| r(m(X1,X4,X7),m(X2,X5,X8),m(X3,X6,X9)) ),
inference(fof_simplification,[status(thm)],[sos_008]) ).
cnf(c_0_26,plain,
( ~ r(X1,X2,X3)
| r(u(X1,X1,a),u(X2,X2,b),u(X3,X3,a)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,axiom,
r(a,a,b),
sos_011 ).
cnf(c_0_28,axiom,
u(X1,X1,X1) = X1,
sos_002 ).
cnf(c_0_29,plain,
( ~ r(X1,X3,X5)
| ~ r(X2,X4,X6)
| r(u(X1,X2,b),u(X3,X4,a),u(X5,X6,a)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
u(X1,X2,X2) = u(X1,X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
( ~ r(X1,X2,X3)
| r(u(X1,X1,b),u(X2,X2,a),u(X3,X3,a)) ),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_32,plain,
( ~ r(X7,X8,X9)
| ~ r(X4,X5,X6)
| ~ r(X1,X2,X3)
| r(m(X1,X4,X7),m(X2,X5,X8),m(X3,X6,X9)) ),
c_0_25 ).
cnf(c_0_33,plain,
r(a,u(a,a,b),u(a,a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_23]) ).
cnf(c_0_34,plain,
( ~ r(X1,X2,X3)
| r(u(X1,a,b),u(X2,b,a),u(X3,a,a)) ),
inference(spm,[status(thm)],[c_0_29,c_0_20]) ).
cnf(c_0_35,plain,
u(X1,X2,X2) = u(X2,X1,X1),
inference(spm,[status(thm)],[c_0_24,c_0_30]) ).
cnf(c_0_36,axiom,
u(X1,X1,X2) = u(X1,X2,X1),
sos_004 ).
cnf(c_0_37,plain,
r(u(a,a,b),a,u(a,a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_27]),c_0_28]),c_0_23]) ).
cnf(c_0_38,plain,
( ~ r(X1,X3,X5)
| ~ r(X2,X4,X6)
| r(m(X1,X2,a),m(X3,X4,u(a,a,b)),m(X5,X6,u(a,a,b))) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
r(u(a,a,b),u(a,a,b),u(a,a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_27]),c_0_35]),c_0_30]),c_0_36]) ).
cnf(c_0_40,axiom,
m(X1,X2,X2) = X1,
sos_001 ).
cnf(c_0_41,plain,
( ~ r(X1,X3,X5)
| ~ r(X2,X4,X6)
| r(m(X1,X2,u(a,a,b)),m(X3,X4,a),m(X5,X6,u(a,a,b))) ),
inference(spm,[status(thm)],[c_0_32,c_0_37]) ).
cnf(c_0_42,plain,
( ~ r(X1,X2,X3)
| r(m(X1,u(a,a,b),a),X2,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_40]) ).
cnf(c_0_43,plain,
r(u(a,a,b),u(a,a,b),a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_20]),c_0_28]),c_0_23]) ).
cnf(c_0_44,axiom,
m(X1,X1,X2) = X2,
sos ).
cnf(c_0_45,negated_conjecture,
~ r(a,a,a),
inference(fof_simplification,[status(thm)],[goals]) ).
cnf(c_0_46,plain,
( ~ r(X1,X2,X3)
| r(X1,m(X2,u(a,a,b),a),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_39]),c_0_40]),c_0_40]) ).
cnf(c_0_47,plain,
r(a,u(a,a,b),a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_48,negated_conjecture,
~ r(a,a,a),
c_0_45 ).
cnf(c_0_49,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_44]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG440-1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n002.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 13:24:02 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.64/0.51 % Version: 3.5.1
% 0.64/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.64/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.64/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.64/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.64/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.64/0.51 % Starting sh5l with 300s (1) cores
% 0.64/0.51 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3377950 completed with status 0
% 0.64/0.51 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.64/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.64/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.64/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.64/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.64/0.51 % No SInE strategy applied
% 0.64/0.51 % Search class: FHUSM-FFSS33-SFFFFFNN
% 0.64/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.64/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.64/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.64/0.51 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S2k with 136s (1) cores
% 0.64/0.51 % Starting new_bool_3 with 136s (1) cores
% 0.64/0.51 % Starting new_bool_1 with 136s (1) cores
% 0.64/0.51 % G-E--_200_B02_F1_AE_CS_SP_PI_S2k with pid 3377958 completed with status 0
% 0.64/0.51 % Result found by G-E--_200_B02_F1_AE_CS_SP_PI_S2k
% 0.64/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.64/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.64/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.64/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.64/0.51 % No SInE strategy applied
% 0.64/0.51 % Search class: FHUSM-FFSS33-SFFFFFNN
% 0.64/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.64/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.64/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.64/0.51 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S2k with 136s (1) cores
% 0.64/0.51 % Preprocessing time : 0.001 s
% 0.64/0.51
% 0.64/0.51 % Proof found!
% 0.64/0.51 % SZS status Unsatisfiable
% 0.64/0.51 % SZS output start CNFRefutation
% See solution above
% 0.64/0.51 % Parsed axioms : 15
% 0.64/0.51 % Removed by relevancy pruning/SinE : 0
% 0.64/0.51 % Initial clauses : 15
% 0.64/0.51 % Removed in clause preprocessing : 1
% 0.64/0.51 % Initial clauses in saturation : 14
% 0.64/0.51 % Processed clauses : 250
% 0.64/0.51 % ...of these trivial : 35
% 0.64/0.51 % ...subsumed : 41
% 0.64/0.51 % ...remaining for further processing : 174
% 0.64/0.51 % Other redundant clauses eliminated : 0
% 0.64/0.51 % Clauses deleted for lack of memory : 0
% 0.64/0.51 % Backward-subsumed : 0
% 0.64/0.51 % Backward-rewritten : 0
% 0.64/0.51 % Generated clauses : 6528
% 0.64/0.51 % ...of the previous two non-redundant : 6296
% 0.64/0.51 % ...aggressively subsumed : 0
% 0.64/0.51 % Contextual simplify-reflections : 0
% 0.64/0.51 % Paramodulations : 6528
% 0.64/0.51 % Factorizations : 0
% 0.64/0.51 % NegExts : 0
% 0.64/0.51 % Equation resolutions : 0
% 0.64/0.51 % Disequality decompositions : 0
% 0.64/0.51 % Total rewrite steps : 3450
% 0.64/0.51 % ...of those cached : 3339
% 0.64/0.51 % Propositional unsat checks : 0
% 0.64/0.51 % Propositional check models : 0
% 0.64/0.51 % Propositional check unsatisfiable : 0
% 0.64/0.51 % Propositional clauses : 0
% 0.64/0.51 % Propositional clauses after purity: 0
% 0.64/0.51 % Propositional unsat core size : 0
% 0.64/0.51 % Propositional preprocessing time : 0.000
% 0.64/0.51 % Propositional encoding time : 0.000
% 0.64/0.51 % Propositional solver time : 0.000
% 0.64/0.51 % Success case prop preproc time : 0.000
% 0.64/0.51 % Success case prop encoding time : 0.000
% 0.64/0.51 % Success case prop solver time : 0.000
% 0.64/0.51 % Current number of processed clauses : 174
% 0.64/0.51 % Positive orientable unit clauses : 87
% 0.64/0.51 % Positive unorientable unit clauses: 9
% 0.64/0.51 % Negative unit clauses : 1
% 0.64/0.51 % Non-unit-clauses : 77
% 0.64/0.51 % Current number of unprocessed clauses: 6031
% 0.64/0.51 % ...number of literals in the above : 7362
% 0.64/0.51 % Current number of archived formulas : 0
% 0.64/0.51 % Current number of archived clauses : 1
% 0.64/0.51 % Clause-clause subsumption calls (NU) : 1367
% 0.64/0.51 % Rec. Clause-clause subsumption calls : 1366
% 0.64/0.51 % Non-unit clause-clause subsumptions : 5
% 0.64/0.51 % Unit Clause-clause subsumption calls : 243
% 0.64/0.51 % Rewrite failures with RHS unbound : 0
% 0.64/0.51 % BW rewrite match attempts : 240
% 0.64/0.51 % BW rewrite match successes : 44
% 0.64/0.51 % Condensation attempts : 0
% 0.64/0.51 % Condensation successes : 0
% 0.64/0.51 % Termbank termtop insertions : 166741
% 0.64/0.51 % Search garbage collected termcells : 16
% 0.64/0.51
% 0.64/0.51 % -------------------------------------------------
% 0.64/0.51 % User time : 0.079 s
% 0.64/0.51 % System time : 0.017 s
% 0.64/0.51 % Total time : 0.097 s
% 0.64/0.51 % Maximum resident set size: 3636 pages
% 0.64/0.51
% 0.64/0.51 % -------------------------------------------------
% 0.64/0.51 % User time : 0.356 s
% 0.64/0.51 % System time : 0.037 s
% 0.64/0.51 % Total time : 0.393 s
% 0.64/0.51 % Maximum resident set size: 4864 pages
% 0.64/0.51 % E exiting
%------------------------------------------------------------------------------