%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP667-3 : 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 : 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 12:40:42 PM UTC 2026
% Result : Unsatisfiable 33.10s 5.62s
% Output : CNFRefutation 33.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of clauses : 61 ( 61 unt; 0 nHn; 4 RR)
% Number of literals : 61 ( 60 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c08,axiom,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
cnf(c01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
cnf(c07,axiom,
mult(mult(X1,X2),mult(mult(X3,X2),X3)) = mult(mult(X1,mult(mult(X2,X3),X2)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
cnf(c02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
cnf(c05,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
cnf(c04,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
cnf(c06,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
cnf(c03,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
cnf(c09,axiom,
mult(f(X1),f(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
cnf(goals,negated_conjecture,
mult(a,mult(b,mult(c,b))) != mult(mult(mult(a,b),c),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_10,axiom,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
c08 ).
cnf(c_0_11,axiom,
mult(X1,ld(X1,X2)) = X2,
c01 ).
cnf(c_0_12,axiom,
mult(mult(X1,X2),mult(mult(X3,X2),X3)) = mult(mult(X1,mult(mult(X2,X3),X2)),X3),
c07 ).
cnf(c_0_13,axiom,
ld(X1,mult(X1,X2)) = X2,
c02 ).
cnf(c_0_14,plain,
mult(X1,mult(ld(X1,X2),X1)) = mult(X2,X1),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,axiom,
mult(X1,unit) = X1,
c05 ).
cnf(c_0_16,axiom,
rd(mult(X1,X2),X2) = X1,
c04 ).
cnf(c_0_17,plain,
mult(mult(X1,mult(X2,mult(X3,X2))),X3) = mult(mult(X1,X2),mult(X3,mult(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_10]),c_0_10]) ).
cnf(c_0_18,plain,
ld(X1,mult(X2,X1)) = mult(ld(X1,X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,axiom,
mult(unit,X1) = X1,
c06 ).
cnf(c_0_20,plain,
ld(X1,X1) = unit,
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_21,plain,
rd(mult(X1,mult(X2,X1)),X1) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_22,axiom,
mult(rd(X1,X2),X2) = X1,
c03 ).
cnf(c_0_23,plain,
rd(mult(mult(X1,X2),mult(X3,mult(X2,X3))),X3) = mult(X1,mult(X2,mult(X3,X2))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
mult(ld(X1,unit),X1) = unit,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_25,plain,
rd(mult(X1,X2),X1) = mult(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
mult(ld(X1,unit),mult(X1,mult(X2,X1))) = mult(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_19]),c_0_25]),c_0_16]) ).
cnf(c_0_27,plain,
mult(ld(X1,rd(X2,X1)),X1) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_28,plain,
mult(mult(X1,mult(X2,X1)),X2) = mult(X1,mult(X2,mult(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_19]) ).
cnf(c_0_29,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_17]),c_0_15]),c_0_19]),c_0_19]) ).
cnf(c_0_30,plain,
mult(ld(X1,unit),X2) = ld(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_11]) ).
cnf(c_0_31,plain,
mult(mult(X1,X2),ld(X2,X1)) = mult(X2,mult(ld(X2,X1),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_14]),c_0_11]) ).
cnf(c_0_32,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
cnf(c_0_33,plain,
ld(X1,mult(X2,X2)) = mult(ld(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_30]) ).
cnf(c_0_34,plain,
mult(mult(X1,rd(X1,X2)),X2) = mult(rd(X1,X2),mult(X2,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
mult(X1,mult(ld(X1,X2),X2)) = mult(X2,X2),
inference(spm,[status(thm)],[c_0_11,c_0_33]) ).
cnf(c_0_36,plain,
rd(mult(rd(X1,X2),mult(X2,X1)),X2) = mult(X1,rd(X1,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_34]) ).
cnf(c_0_37,plain,
mult(rd(X1,X2),mult(X2,X1)) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_38,plain,
ld(mult(X1,X2),mult(X2,mult(ld(X2,X1),X1))) = ld(X2,X1),
inference(spm,[status(thm)],[c_0_13,c_0_31]) ).
cnf(c_0_39,plain,
rd(mult(X1,X1),X2) = mult(X1,rd(X1,X2)),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,plain,
rd(ld(X1,X2),X2) = ld(X1,unit),
inference(spm,[status(thm)],[c_0_16,c_0_30]) ).
cnf(c_0_41,plain,
mult(mult(X1,X2),mult(X1,mult(X2,X1))) = mult(X1,mult(X2,mult(X1,mult(X2,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_17]),c_0_28]) ).
cnf(c_0_42,plain,
mult(ld(mult(X1,X2),X1),X1) = ld(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_35]),c_0_33]) ).
cnf(c_0_43,plain,
mult(X1,rd(X1,mult(X2,X1))) = rd(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_37]),c_0_39]) ).
cnf(c_0_44,plain,
rd(X1,mult(X2,X1)) = ld(X2,unit),
inference(spm,[status(thm)],[c_0_40,c_0_13]) ).
cnf(c_0_45,plain,
mult(mult(ld(X1,X2),X2),X1) = mult(ld(X1,X2),mult(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_11]),c_0_14]) ).
cnf(c_0_46,plain,
mult(X1,mult(ld(X1,X2),mult(X2,X1))) = mult(X2,mult(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_14]),c_0_11]) ).
cnf(c_0_47,plain,
mult(mult(X1,mult(X2,X3)),ld(X3,X2)) = mult(mult(X1,X3),mult(ld(X3,X2),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_11]) ).
cnf(c_0_48,plain,
ld(mult(X1,X2),X1) = ld(X2,unit),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_42]),c_0_40]) ).
cnf(c_0_49,plain,
mult(X1,ld(X2,unit)) = rd(X1,X2),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_33]),c_0_45]),c_0_46]) ).
cnf(c_0_51,axiom,
mult(f(X1),f(X1)) = X1,
c09 ).
cnf(c_0_52,plain,
rd(mult(X1,mult(X2,mult(X2,X3))),X3) = mult(mult(X1,X3),mult(ld(X3,X2),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_30]),c_0_47]) ).
cnf(c_0_53,plain,
mult(f(X1),mult(f(X1),X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
mult(ld(X1,f(X2)),f(X2)) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_51]) ).
cnf(c_0_55,plain,
rd(mult(X1,mult(X2,X3)),X3) = mult(mult(X1,X3),ld(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_56,negated_conjecture,
mult(a,mult(b,mult(c,b))) != mult(mult(mult(a,b),c),b),
inference(fof_simplification,[status(thm)],[goals]) ).
cnf(c_0_57,plain,
mult(mult(mult(X1,X2),ld(X2,X3)),X2) = mult(X1,mult(X3,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_55]) ).
cnf(c_0_58,negated_conjecture,
mult(a,mult(b,mult(c,b))) != mult(mult(mult(a,b),c),b),
c_0_56 ).
cnf(c_0_59,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(X2,mult(X3,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_13]),c_0_10]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP667-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n011.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 20 20:31:25 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.55 Running first-order theorem proving
% 0.24/0.55 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
% 33.10/5.62 % Version: 3.5.1
% 33.10/5.62 % Preprocessing class: FSSSSMSSSSSNFFN.
% 33.10/5.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.10/5.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 33.10/5.62 % Starting new_bool_3 with 300s (1) cores
% 33.10/5.62 % Starting new_bool_1 with 300s (1) cores
% 33.10/5.62 % Starting sh5l with 300s (1) cores
% 33.10/5.62 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 128445 completed with status 0
% 33.10/5.62 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 33.10/5.62 % Preprocessing class: FSSSSMSSSSSNFFN.
% 33.10/5.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.10/5.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 33.10/5.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 33.10/5.62 % No SInE strategy applied
% 33.10/5.62 % Search class: FUUPM-FFSF21-MFFFFFNN
% 33.10/5.62 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 33.10/5.62 % Starting SubtermCWHack with 136s (1) cores
% 33.10/5.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 33.10/5.62 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 33.10/5.62 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 33.10/5.62 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 33.10/5.62 % G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with pid 128455 completed with status 0
% 33.10/5.62 % Result found by G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y
% 33.10/5.62 % Preprocessing class: FSSSSMSSSSSNFFN.
% 33.10/5.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.10/5.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 33.10/5.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 33.10/5.62 % No SInE strategy applied
% 33.10/5.62 % Search class: FUUPM-FFSF21-MFFFFFNN
% 33.10/5.62 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 33.10/5.62 % Starting SubtermCWHack with 136s (1) cores
% 33.10/5.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 33.10/5.62 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 33.10/5.62 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 33.10/5.62 % Preprocessing time : 0.002 s
% 33.10/5.62
% 33.10/5.62 % Proof found!
% 33.10/5.62 % SZS status Unsatisfiable
% 33.10/5.62 % SZS output start CNFRefutation
% See solution above
% 33.10/5.62 % Parsed axioms : 10
% 33.10/5.62 % Removed by relevancy pruning/SinE : 0
% 33.10/5.62 % Initial clauses : 10
% 33.10/5.62 % Removed in clause preprocessing : 0
% 33.10/5.62 % Initial clauses in saturation : 10
% 33.10/5.62 % Processed clauses : 3303
% 33.10/5.62 % ...of these trivial : 2160
% 33.10/5.62 % ...subsumed : 379
% 33.10/5.62 % ...remaining for further processing : 764
% 33.10/5.62 % Other redundant clauses eliminated : 0
% 33.10/5.62 % Clauses deleted for lack of memory : 0
% 33.10/5.62 % Backward-subsumed : 0
% 33.10/5.62 % Backward-rewritten : 233
% 33.10/5.62 % Generated clauses : 186965
% 33.10/5.62 % ...of the previous two non-redundant : 150020
% 33.10/5.62 % ...aggressively subsumed : 0
% 33.10/5.62 % Contextual simplify-reflections : 0
% 33.10/5.62 % Paramodulations : 186965
% 33.10/5.62 % Factorizations : 0
% 33.10/5.62 % NegExts : 0
% 33.10/5.62 % Equation resolutions : 0
% 33.10/5.62 % Disequality decompositions : 0
% 33.10/5.62 % Total rewrite steps : 488664
% 33.10/5.62 % ...of those cached : 432779
% 33.10/5.62 % Propositional unsat checks : 0
% 33.10/5.62 % Propositional check models : 0
% 33.10/5.62 % Propositional check unsatisfiable : 0
% 33.10/5.62 % Propositional clauses : 0
% 33.10/5.62 % Propositional clauses after purity: 0
% 33.10/5.62 % Propositional unsat core size : 0
% 33.10/5.62 % Propositional preprocessing time : 0.000
% 33.10/5.62 % Propositional encoding time : 0.000
% 33.10/5.62 % Propositional solver time : 0.000
% 33.10/5.62 % Success case prop preproc time : 0.000
% 33.10/5.62 % Success case prop encoding time : 0.000
% 33.10/5.62 % Success case prop solver time : 0.000
% 33.10/5.62 % Current number of processed clauses : 531
% 33.10/5.62 % Positive orientable unit clauses : 526
% 33.10/5.62 % Positive unorientable unit clauses: 5
% 33.10/5.62 % Negative unit clauses : 0
% 33.10/5.62 % Non-unit-clauses : 0
% 33.10/5.62 % Current number of unprocessed clauses: 146206
% 33.10/5.62 % ...number of literals in the above : 146206
% 33.10/5.62 % Current number of archived formulas : 0
% 33.10/5.62 % Current number of archived clauses : 233
% 33.10/5.62 % Clause-clause subsumption calls (NU) : 0
% 33.10/5.62 % Rec. Clause-clause subsumption calls : 0
% 33.10/5.62 % Non-unit clause-clause subsumptions : 0
% 33.10/5.62 % Unit Clause-clause subsumption calls : 21
% 33.10/5.62 % Rewrite failures with RHS unbound : 0
% 33.10/5.62 % BW rewrite match attempts : 3079
% 33.10/5.62 % BW rewrite match successes : 217
% 33.10/5.62 % Condensation attempts : 3303
% 33.10/5.62 % Condensation successes : 0
% 33.10/5.62 % Termbank termtop insertions : 2982421
% 33.10/5.62 % Search garbage collected termcells : 2
% 33.10/5.62
% 33.10/5.62 % -------------------------------------------------
% 33.10/5.62 % User time : 4.701 s
% 33.10/5.62 % System time : 0.189 s
% 33.10/5.62 % Total time : 4.890 s
% 33.10/5.62 % Maximum resident set size: 3636 pages
% 33.10/5.62
% 33.10/5.62 % -------------------------------------------------
% 33.10/5.62 % User time : 22.243 s
% 33.10/5.62 % System time : 0.823 s
% 33.10/5.62 % Total time : 23.066 s
% 33.10/5.62 % Maximum resident set size: 4608 pages
% 33.10/5.62 % E exiting
%------------------------------------------------------------------------------