%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : BOO072-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:07:21 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.60s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 4 RR)
% Number of literals : 37 ( 36 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 72 ( 23 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(dn1,axiom,
inverse(add(inverse(add(inverse(add(X1,X2)),X3)),inverse(add(X1,inverse(add(inverse(X3),inverse(add(X3,X4)))))))) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dn1) ).
cnf(huntinton_1,negated_conjecture,
add(b,a) != add(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',huntinton_1) ).
cnf(c_0_2,axiom,
inverse(add(inverse(add(inverse(add(X1,X2)),X3)),inverse(add(X1,inverse(add(inverse(X3),inverse(add(X3,X4)))))))) = X3,
dn1 ).
cnf(c_0_3,plain,
inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X1)),X2)),X1)),X3)),inverse(X1))),X1)) = inverse(X1),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
inverse(add(inverse(add(X1,inverse(X1))),X1)) = inverse(X1),
inference(spm,[status(thm)],[c_0_3,c_0_2]) ).
cnf(c_0_5,plain,
inverse(add(inverse(X1),inverse(add(X1,inverse(add(inverse(X1),inverse(add(X1,X2)))))))) = X1,
inference(spm,[status(thm)],[c_0_2,c_0_4]) ).
cnf(c_0_6,plain,
inverse(add(inverse(add(inverse(add(X1,X2)),X3)),inverse(add(X1,X3)))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_5]) ).
cnf(c_0_7,plain,
inverse(add(inverse(add(X1,X2)),inverse(add(inverse(X1),X2)))) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_8,plain,
inverse(add(inverse(add(X1,X2)),inverse(add(inverse(add(X3,X1)),X2)))) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
inverse(add(inverse(add(inverse(X1),X1)),inverse(X1))) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_3]) ).
cnf(c_0_10,plain,
inverse(add(X1,inverse(add(inverse(X1),inverse(X1))))) = inverse(X1),
inference(spm,[status(thm)],[c_0_6,c_0_9]) ).
cnf(c_0_11,plain,
inverse(add(inverse(X1),inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_10]),c_0_10]) ).
cnf(c_0_12,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_10]),c_0_11]),c_0_11]) ).
cnf(c_0_13,plain,
inverse(add(inverse(add(inverse(add(X1,X2)),X1)),inverse(X1))) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_12]) ).
cnf(c_0_14,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
inverse(add(inverse(X1),inverse(add(X1,X1)))) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_16,plain,
inverse(add(X1,add(X2,X1))) = inverse(add(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_6]),c_0_14]) ).
cnf(c_0_17,plain,
add(X1,add(X2,X1)) = add(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_12]),c_0_16]),c_0_12]),c_0_14]) ).
cnf(c_0_18,plain,
add(inverse(add(X1,X2)),inverse(add(inverse(X1),X2))) = inverse(X2),
inference(spm,[status(thm)],[c_0_14,c_0_7]) ).
cnf(c_0_19,plain,
add(inverse(add(inverse(X1),X2)),inverse(X2)) = inverse(X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
add(inverse(add(inverse(X1),inverse(X2))),X2) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_21,plain,
add(inverse(add(X1,inverse(X2))),X2) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_22,plain,
inverse(add(inverse(X1),inverse(add(X2,X1)))) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_21]) ).
cnf(c_0_23,plain,
inverse(add(inverse(add(X1,X2)),inverse(add(inverse(add(inverse(add(X3,X4)),X1)),inverse(add(inverse(X2),inverse(add(X2,X5)))))))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_24,plain,
add(inverse(X1),inverse(add(X2,X1))) = inverse(X1),
inference(spm,[status(thm)],[c_0_14,c_0_22]) ).
cnf(c_0_25,plain,
inverse(add(inverse(add(inverse(add(X1,X2)),X1)),inverse(add(X1,X2)))) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_6]) ).
cnf(c_0_26,plain,
add(add(X1,X2),X1) = add(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_14]),c_0_14]) ).
cnf(c_0_27,plain,
add(X1,inverse(add(X2,inverse(X1)))) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_28,plain,
inverse(add(X1,inverse(add(inverse(add(X2,X3)),inverse(add(add(X2,inverse(add(inverse(X1),inverse(add(X1,X4))))),inverse(add(inverse(add(X2,inverse(add(inverse(X1),inverse(add(X1,X4)))))),X5)))))))) = inverse(add(X2,inverse(add(inverse(X1),inverse(add(X1,X4)))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_2]),c_0_14]) ).
cnf(c_0_29,plain,
add(inverse(X1),inverse(add(X1,X2))) = inverse(X1),
inference(spm,[status(thm)],[c_0_24,c_0_26]) ).
cnf(c_0_30,plain,
add(X1,inverse(add(inverse(X1),X2))) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_31,plain,
inverse(add(X1,inverse(X2))) = inverse(add(inverse(X2),X1)),
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_28,c_0_29]),c_0_14]),c_0_29]),c_0_14]),c_0_29]),c_0_14]),c_0_30]),c_0_30]),c_0_29]),c_0_14]) ).
cnf(c_0_32,negated_conjecture,
add(b,a) != add(a,b),
inference(fof_simplification,[status(thm)],[huntinton_1]) ).
cnf(c_0_33,plain,
add(X1,inverse(X2)) = add(inverse(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_31]),c_0_14]) ).
cnf(c_0_34,negated_conjecture,
add(b,a) != add(a,b),
c_0_32 ).
cnf(c_0_35,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_33,c_0_14]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO072-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n001.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 13:57:29 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 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
% 0.22/0.60 % Version: 3.5.1
% 0.22/0.60 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.22/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.22/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.60 % Starting sh5l with 300s (1) cores
% 0.22/0.60 % new_bool_3 with pid 3295707 completed with status 9
% 0.22/0.60 % new_bool_1 with pid 3295713 completed with status 9
% 0.22/0.60 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3295706 completed with status 0
% 0.22/0.60 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.22/0.60 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.22/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.22/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.60 % No SInE strategy applied
% 0.22/0.60 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.22/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.22/0.60 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.22/0.60 % Starting new_bool_3 with 136s (1) cores
% 0.22/0.60 % Starting new_bool_1 with 136s (1) cores
% 0.22/0.60 % SubtermCWHack with pid 3295708 completed with status 0
% 0.22/0.60 % Result found by SubtermCWHack
% 0.22/0.60 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.22/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.22/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.60 % No SInE strategy applied
% 0.22/0.60 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.22/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.60 % Preprocessing time : 0.002 s
% 0.22/0.60
% 0.22/0.60 % Proof found!
% 0.22/0.60 % SZS status Unsatisfiable
% 0.22/0.60 % SZS output start CNFRefutation
% See solution above
% 0.22/0.60 % Parsed axioms : 2
% 0.22/0.60 % Removed by relevancy pruning/SinE : 0
% 0.22/0.60 % Initial clauses : 2
% 0.22/0.60 % Removed in clause preprocessing : 0
% 0.22/0.60 % Initial clauses in saturation : 2
% 0.22/0.60 % Processed clauses : 118
% 0.22/0.60 % ...of these trivial : 52
% 0.22/0.60 % ...subsumed : 0
% 0.22/0.60 % ...remaining for further processing : 66
% 0.22/0.60 % Other redundant clauses eliminated : 0
% 0.22/0.60 % Clauses deleted for lack of memory : 0
% 0.22/0.60 % Backward-subsumed : 2
% 0.22/0.60 % Backward-rewritten : 46
% 0.22/0.60 % Generated clauses : 5052
% 0.22/0.60 % ...of the previous two non-redundant : 3718
% 0.22/0.60 % ...aggressively subsumed : 0
% 0.22/0.60 % Contextual simplify-reflections : 0
% 0.22/0.60 % Paramodulations : 5052
% 0.22/0.60 % Factorizations : 0
% 0.22/0.60 % NegExts : 0
% 0.22/0.60 % Equation resolutions : 0
% 0.22/0.60 % Disequality decompositions : 0
% 0.22/0.60 % Total rewrite steps : 8234
% 0.22/0.60 % ...of those cached : 7467
% 0.22/0.60 % Propositional unsat checks : 0
% 0.22/0.60 % Propositional check models : 0
% 0.22/0.60 % Propositional check unsatisfiable : 0
% 0.22/0.60 % Propositional clauses : 0
% 0.22/0.60 % Propositional clauses after purity: 0
% 0.22/0.60 % Propositional unsat core size : 0
% 0.22/0.60 % Propositional preprocessing time : 0.000
% 0.22/0.60 % Propositional encoding time : 0.000
% 0.22/0.60 % Propositional solver time : 0.000
% 0.22/0.60 % Success case prop preproc time : 0.000
% 0.22/0.60 % Success case prop encoding time : 0.000
% 0.22/0.60 % Success case prop solver time : 0.000
% 0.22/0.60 % Current number of processed clauses : 18
% 0.22/0.60 % Positive orientable unit clauses : 17
% 0.22/0.60 % Positive unorientable unit clauses: 1
% 0.22/0.60 % Negative unit clauses : 0
% 0.22/0.60 % Non-unit-clauses : 0
% 0.22/0.60 % Current number of unprocessed clauses: 3448
% 0.22/0.60 % ...number of literals in the above : 3448
% 0.22/0.60 % Current number of archived formulas : 0
% 0.22/0.60 % Current number of archived clauses : 48
% 0.22/0.60 % Clause-clause subsumption calls (NU) : 0
% 0.22/0.60 % Rec. Clause-clause subsumption calls : 0
% 0.22/0.60 % Non-unit clause-clause subsumptions : 0
% 0.22/0.60 % Unit Clause-clause subsumption calls : 39
% 0.22/0.60 % Rewrite failures with RHS unbound : 0
% 0.22/0.60 % BW rewrite match attempts : 727
% 0.22/0.60 % BW rewrite match successes : 151
% 0.22/0.60 % Condensation attempts : 0
% 0.22/0.60 % Condensation successes : 0
% 0.22/0.60 % Termbank termtop insertions : 163505
% 0.22/0.60 % Search garbage collected termcells : 2
% 0.22/0.60
% 0.22/0.60 % -------------------------------------------------
% 0.22/0.60 % User time : 0.085 s
% 0.22/0.60 % System time : 0.012 s
% 0.22/0.60 % Total time : 0.097 s
% 0.22/0.60 % Maximum resident set size: 3380 pages
% 0.22/0.60
% 0.22/0.60 % -------------------------------------------------
% 0.22/0.60 % User time : 0.419 s
% 0.22/0.60 % System time : 0.084 s
% 0.22/0.60 % Total time : 0.503 s
% 0.22/0.60 % Maximum resident set size: 4608 pages
% 0.22/0.60 % E exiting
%------------------------------------------------------------------------------