%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP748-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:41:10 PM UTC 2026
% Result : Unsatisfiable 0.31s 1.05s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of clauses : 46 ( 37 unt; 6 nHn; 8 RR)
% Number of literals : 55 ( 54 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f07,axiom,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
cnf(f10,axiom,
mult(i(X1),X1) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f10) ).
cnf(f06,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
cnf(f01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
cnf(f11,axiom,
( mult(i(X1),mult(X1,X2)) = X2
| mult(X1,X2) = mult(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f11) ).
cnf(f08,axiom,
mult(mult(X1,X2),i(X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
cnf(f09,axiom,
mult(X1,i(X1)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
cnf(f02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
cnf(goals,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_9,axiom,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
f07 ).
cnf(c_0_10,axiom,
mult(i(X1),X1) = unit,
f10 ).
cnf(c_0_11,axiom,
mult(unit,X1) = X1,
f06 ).
cnf(c_0_12,plain,
mult(i(X1),mult(mult(X1,X2),X1)) = mult(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_13,axiom,
mult(X1,ld(X1,X2)) = X2,
f01 ).
cnf(c_0_14,axiom,
( mult(i(X1),mult(X1,X2)) = X2
| mult(X1,X2) = mult(X2,X1) ),
f11 ).
cnf(c_0_15,plain,
mult(ld(X1,X2),X1) = mult(i(X1),mult(X2,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
mult(mult(X1,X2),i(X2)) = X1,
f08 ).
cnf(c_0_17,axiom,
mult(X1,i(X1)) = unit,
f09 ).
cnf(c_0_18,plain,
( ld(X1,X2) = mult(i(X1),X2)
| mult(i(X1),mult(X2,X1)) = X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_15]) ).
cnf(c_0_19,plain,
i(i(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_11]) ).
cnf(c_0_20,axiom,
ld(X1,mult(X1,X2)) = X2,
f02 ).
cnf(c_0_21,plain,
( mult(X1,mult(X2,i(X1))) = X2
| ld(X1,X2) = mult(i(X1),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_18]),c_0_19]),c_0_16]) ).
cnf(c_0_22,plain,
( ld(X1,X2) = mult(X2,i(X1))
| ld(X1,X2) = mult(i(X1),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
( mult(i(X1),X2) != mult(X2,i(X1))
| ld(X1,X2) = mult(X2,i(X1)) ),
inference(ef,[status(thm)],[c_0_22]) ).
cnf(c_0_24,plain,
( mult(i(X1),X2) != mult(X2,i(X1))
| mult(X1,mult(X2,i(X1))) = X2 ),
inference(spm,[status(thm)],[c_0_13,c_0_23]) ).
cnf(c_0_25,plain,
mult(mult(X1,i(X2)),X2) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_26,plain,
mult(mult(X1,mult(mult(X2,X3),X2)),i(X2)) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_16,c_0_9]) ).
cnf(c_0_27,plain,
( mult(i(X1),mult(X2,X1)) != X2
| mult(X1,X2) = mult(X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_19]),c_0_19]) ).
cnf(c_0_28,plain,
( mult(mult(X1,X2),i(X1)) = X2
| mult(i(X1),mult(X1,X2)) = X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_18]),c_0_10]),c_0_11]),c_0_20]) ).
cnf(c_0_29,plain,
mult(i(X1),mult(X1,X2)) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_19])]) ).
cnf(c_0_30,plain,
mult(mult(X1,i(X2)),mult(mult(X2,X3),X2)) = mult(mult(X1,X3),X2),
inference(spm,[status(thm)],[c_0_9,c_0_25]) ).
cnf(c_0_31,plain,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_12]),c_0_19]) ).
cnf(c_0_32,plain,
mult(X1,i(mult(X2,X1))) = i(X2),
inference(spm,[status(thm)],[c_0_16,c_0_29]) ).
cnf(c_0_33,plain,
mult(mult(X1,i(X2)),mult(X2,mult(X3,X2))) = mult(mult(X1,X3),X2),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
i(mult(X1,X2)) = mult(i(X2),i(X1)),
inference(spm,[status(thm)],[c_0_29,c_0_32]) ).
cnf(c_0_35,plain,
mult(mult(X1,mult(X2,i(X1))),X1) = ld(i(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_15]),c_0_19]) ).
cnf(c_0_36,plain,
ld(X1,X2) = mult(i(X1),X2),
inference(spm,[status(thm)],[c_0_29,c_0_13]) ).
cnf(c_0_37,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
inference(fof_simplification,[status(thm)],[goals]) ).
cnf(c_0_38,plain,
mult(mult(X1,i(X2)),mult(mult(X2,X3),X1)) = mult(X1,mult(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_33]),c_0_34]),c_0_19]) ).
cnf(c_0_39,plain,
mult(mult(X1,mult(X2,i(X1))),X1) = mult(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_19]) ).
cnf(c_0_40,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
c_0_37 ).
cnf(c_0_41,plain,
mult(mult(X1,X2),mult(X3,X1)) = mult(X1,mult(mult(X2,X3),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_29]),c_0_19]) ).
cnf(c_0_42,plain,
mult(mult(X1,X2),i(X1)) = mult(X1,mult(X2,i(X1))),
inference(spm,[status(thm)],[c_0_16,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
mult(mult(a,mult(b,a)),c) != mult(a,mult(b,mult(a,c))),
inference(rw,[status(thm)],[c_0_40,c_0_31]) ).
cnf(c_0_44,plain,
mult(mult(X1,mult(X2,X1)),X3) = mult(X1,mult(X2,mult(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_41]),c_0_42]),c_0_16]),c_0_31]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP748-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 % Computer : n026.cluster.edu
% 0.21/0.48 % Model : x86_64 x86_64
% 0.21/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.48 % Memory : 8046.5625MB
% 0.21/0.48 % OS : Linux 6.8.0-71-generic
% 0.21/0.48 % CPULimit : 300
% 0.21/0.48 % WCLimit : 300
% 0.21/0.48 % DateTime : Sun Sep 20 20:39:52 UTC 2026
% 0.21/0.49 % CPUTime :
% 0.21/0.49 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.58 Running first-order theorem proving
% 0.25/0.58 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
% 0.31/1.05 % Version: 3.5.1
% 0.31/1.05 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.31/1.05 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/1.05 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.31/1.05 % Starting new_bool_3 with 300s (1) cores
% 0.31/1.05 % Starting new_bool_1 with 300s (1) cores
% 0.31/1.05 % Starting sh5l with 300s (1) cores
% 0.31/1.05 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 556841 completed with status 0
% 0.31/1.05 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.31/1.05 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.31/1.05 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/1.05 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.31/1.05 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.31/1.05 % No SInE strategy applied
% 0.31/1.05 % Search class: FGUPM-FFSF21-MFFFFFNN
% 0.31/1.05 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.31/1.05 % Starting SubtermCWHack with 136s (1) cores
% 0.31/1.05 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.31/1.05 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 136s (1) cores
% 0.31/1.05 % Starting new_bool_3 with 136s (1) cores
% 0.31/1.05 % Starting new_bool_1 with 136s (1) cores
% 0.31/1.05 % C12_02_nc_SAT001_MinMin_p005000_rr with pid 556848 completed with status 0
% 0.31/1.05 % Result found by C12_02_nc_SAT001_MinMin_p005000_rr
% 0.31/1.05 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.31/1.05 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/1.05 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.31/1.05 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.31/1.05 % No SInE strategy applied
% 0.31/1.05 % Search class: FGUPM-FFSF21-MFFFFFNN
% 0.31/1.05 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.31/1.05 % Starting SubtermCWHack with 136s (1) cores
% 0.31/1.05 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.31/1.05 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 136s (1) cores
% 0.31/1.05 % Preprocessing time : 0.001 s
% 0.31/1.05 % Presaturation interreduction done
% 0.31/1.05
% 0.31/1.05 % Proof found!
% 0.31/1.05 % SZS status Unsatisfiable
% 0.31/1.05 % SZS output start CNFRefutation
% See solution above
% 0.31/1.05 % Parsed axioms : 12
% 0.31/1.05 % Removed by relevancy pruning/SinE : 0
% 0.31/1.05 % Initial clauses : 12
% 0.31/1.05 % Removed in clause preprocessing : 0
% 0.31/1.05 % Initial clauses in saturation : 12
% 0.31/1.05 % Processed clauses : 894
% 0.31/1.05 % ...of these trivial : 167
% 0.31/1.05 % ...subsumed : 451
% 0.31/1.05 % ...remaining for further processing : 276
% 0.31/1.05 % Other redundant clauses eliminated : 0
% 0.31/1.05 % Clauses deleted for lack of memory : 0
% 0.31/1.05 % Backward-subsumed : 11
% 0.31/1.05 % Backward-rewritten : 105
% 0.31/1.05 % Generated clauses : 24185
% 0.31/1.05 % ...of the previous two non-redundant : 17729
% 0.31/1.05 % ...aggressively subsumed : 0
% 0.31/1.05 % Contextual simplify-reflections : 0
% 0.31/1.05 % Paramodulations : 24172
% 0.31/1.05 % Factorizations : 2
% 0.31/1.05 % NegExts : 0
% 0.31/1.05 % Equation resolutions : 11
% 0.31/1.05 % Disequality decompositions : 0
% 0.31/1.05 % Total rewrite steps : 97348
% 0.31/1.05 % ...of those cached : 93080
% 0.31/1.05 % Propositional unsat checks : 0
% 0.31/1.05 % Propositional check models : 0
% 0.31/1.05 % Propositional check unsatisfiable : 0
% 0.31/1.05 % Propositional clauses : 0
% 0.31/1.05 % Propositional clauses after purity: 0
% 0.31/1.05 % Propositional unsat core size : 0
% 0.31/1.05 % Propositional preprocessing time : 0.000
% 0.31/1.05 % Propositional encoding time : 0.000
% 0.31/1.05 % Propositional solver time : 0.000
% 0.31/1.05 % Success case prop preproc time : 0.000
% 0.31/1.05 % Success case prop encoding time : 0.000
% 0.31/1.05 % Success case prop solver time : 0.000
% 0.31/1.05 % Current number of processed clauses : 148
% 0.31/1.05 % Positive orientable unit clauses : 88
% 0.31/1.05 % Positive unorientable unit clauses: 0
% 0.31/1.05 % Negative unit clauses : 0
% 0.31/1.05 % Non-unit-clauses : 60
% 0.31/1.05 % Current number of unprocessed clauses: 16111
% 0.31/1.05 % ...number of literals in the above : 23577
% 0.31/1.05 % Current number of archived formulas : 0
% 0.31/1.05 % Current number of archived clauses : 128
% 0.31/1.05 % Clause-clause subsumption calls (NU) : 6684
% 0.31/1.05 % Rec. Clause-clause subsumption calls : 4848
% 0.31/1.05 % Non-unit clause-clause subsumptions : 451
% 0.31/1.05 % Unit Clause-clause subsumption calls : 133
% 0.31/1.05 % Rewrite failures with RHS unbound : 0
% 0.31/1.05 % BW rewrite match attempts : 825
% 0.31/1.05 % BW rewrite match successes : 85
% 0.31/1.05 % Condensation attempts : 0
% 0.31/1.05 % Condensation successes : 0
% 0.31/1.05 % Termbank termtop insertions : 484627
% 0.31/1.05 % Search garbage collected termcells : 2
% 0.31/1.05
% 0.31/1.05 % -------------------------------------------------
% 0.31/1.05 % User time : 0.403 s
% 0.31/1.05 % System time : 0.024 s
% 0.31/1.05 % Total time : 0.427 s
% 0.31/1.05 % Maximum resident set size: 3636 pages
% 0.31/1.05
% 0.31/1.05 % -------------------------------------------------
% 0.31/1.05 % User time : 1.942 s
% 0.31/1.05 % System time : 0.111 s
% 0.31/1.05 % Total time : 2.053 s
% 0.31/1.05 % Maximum resident set size: 4864 pages
% 0.31/1.05 % E exiting
%------------------------------------------------------------------------------