%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP682-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:40:44 PM UTC 2026
% Result : Unsatisfiable 0.35s 0.65s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of clauses : 58 ( 58 unt; 0 nHn; 7 RR)
% Number of literals : 58 ( 57 equ; 6 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f02,axiom,
rd(mult(X1,X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
cnf(f04,axiom,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
cnf(f01,axiom,
ld(X1,mult(X1,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
cnf(f03,axiom,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
cnf(f07,axiom,
ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
cnf(f05,axiom,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
cnf(f06,axiom,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
cnf(goal,negated_conjecture,
ld(ld(x0,x1),mult(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c_0_8,axiom,
rd(mult(X1,X1),X1) = X1,
f02 ).
cnf(c_0_9,axiom,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
f04 ).
cnf(c_0_10,axiom,
ld(X1,mult(X1,X1)) = X1,
f01 ).
cnf(c_0_11,axiom,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
f03 ).
cnf(c_0_12,plain,
mult(rd(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,axiom,
ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
f07 ).
cnf(c_0_14,plain,
mult(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
mult(rd(rd(X1,X1),X1),X1) = rd(X1,X1),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_16,plain,
mult(rd(rd(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_11]),c_0_9]) ).
cnf(c_0_17,plain,
mult(X1,ld(X1,ld(X1,X1))) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_18,axiom,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
f05 ).
cnf(c_0_19,plain,
rd(X1,X1) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_20,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_11]),c_0_11]) ).
cnf(c_0_21,plain,
mult(ld(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_22,axiom,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
f06 ).
cnf(c_0_23,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(mult(X1,ld(X1,ld(X3,X3))),X3),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
mult(rd(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,mult(rd(X2,X4),X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_9]),c_0_9]) ).
cnf(c_0_25,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_17]),c_0_21]) ).
cnf(c_0_26,plain,
mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(ld(X1,X1),mult(rd(X1,X3),X3)),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_27,plain,
mult(rd(ld(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_28,plain,
mult(mult(X1,ld(X1,X2)),ld(mult(X1,ld(X1,X2)),X1)) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_11]) ).
cnf(c_0_29,plain,
mult(ld(ld(X1,X1),X2),ld(ld(ld(X1,X1),X2),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_14]),c_0_21]) ).
cnf(c_0_30,plain,
mult(rd(X1,rd(X2,X1)),rd(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_19]),c_0_21]),c_0_21]) ).
cnf(c_0_31,plain,
mult(rd(X1,ld(X1,X1)),ld(X1,X1)) = rd(X1,ld(X1,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_32,plain,
mult(X1,ld(X1,ld(ld(X1,X1),ld(X1,X1)))) = ld(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_21]) ).
cnf(c_0_33,plain,
mult(X1,ld(X1,ld(ld(X1,X1),X2))) = ld(ld(X1,X1),X2),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(X1,mult(X1,ld(X1,ld(X3,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_14]),c_0_27]) ).
cnf(c_0_35,plain,
rd(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_19]),c_0_31]) ).
cnf(c_0_36,plain,
ld(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
mult(X1,mult(X1,ld(X1,ld(X2,X2)))) = mult(rd(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_38,plain,
mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(rd(X1,X3),X3),
inference(rw,[status(thm)],[c_0_34,c_0_37]) ).
cnf(c_0_39,plain,
mult(rd(mult(X1,X2),X3),X3) = mult(X1,mult(rd(X2,X3),X3)),
inference(rw,[status(thm)],[c_0_24,c_0_38]) ).
cnf(c_0_40,plain,
mult(ld(X1,X2),ld(ld(X1,X2),ld(X1,X1))) = ld(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_33]),c_0_21]) ).
cnf(c_0_41,negated_conjecture,
ld(ld(x0,x1),mult(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
inference(fof_simplification,[status(thm)],[goal]) ).
cnf(c_0_42,plain,
mult(mult(rd(X1,X2),X2),X2) = mult(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_9]),c_0_19]),c_0_21]) ).
cnf(c_0_43,plain,
mult(ld(ld(X1,X2),X3),ld(ld(ld(X1,X2),X3),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_40]),c_0_21]) ).
cnf(c_0_44,negated_conjecture,
ld(ld(x0,x1),mult(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
c_0_41 ).
cnf(c_0_45,plain,
mult(mult(X1,ld(X1,ld(X2,X2))),X2) = mult(ld(X1,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_16]),c_0_19]) ).
cnf(c_0_46,plain,
mult(X1,ld(X1,ld(ld(X1,X2),X3))) = ld(ld(X1,X2),X3),
inference(spm,[status(thm)],[c_0_28,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
mult(ld(x0,x1),ld(ld(x0,x1),x2)) != mult(x0,ld(x0,x2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_11]),c_0_11]) ).
cnf(c_0_48,plain,
mult(ld(X1,X1),ld(ld(X1,X1),X1)) = ld(ld(X1,X1),X1),
inference(spm,[status(thm)],[c_0_11,c_0_21]) ).
cnf(c_0_49,plain,
mult(ld(X1,X1),ld(X1,X2)) = ld(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_21]) ).
cnf(c_0_50,plain,
mult(ld(X1,X2),ld(ld(X1,X2),ld(X1,X3))) = ld(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_46]),c_0_21]) ).
cnf(c_0_51,negated_conjecture,
mult(mult(x0,ld(x0,ld(x2,x2))),x2) != mult(x0,ld(x0,x2)),
inference(rw,[status(thm)],[c_0_47,c_0_23]) ).
cnf(c_0_52,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(ld(X1,X1),X3),
inference(rw,[status(thm)],[c_0_23,c_0_45]) ).
cnf(c_0_53,plain,
ld(ld(X1,X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_23]),c_0_17]),c_0_21]) ).
cnf(c_0_54,plain,
ld(ld(X1,X1),ld(X1,X2)) = ld(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_49]),c_0_50]) ).
cnf(c_0_55,negated_conjecture,
mult(ld(x0,x0),x2) != mult(x0,ld(x0,x2)),
inference(rw,[status(thm)],[c_0_51,c_0_45]) ).
cnf(c_0_56,plain,
mult(ld(X1,X1),X2) = mult(X1,ld(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP682-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n005.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sun Sep 20 20:32:47 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.56 Running first-order theorem proving
% 0.24/0.56 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
% 0.35/0.64 % Version: 3.5.1
% 0.35/0.64 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.35/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.35/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.35/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.35/0.64 % Starting sh5l with 300s (1) cores
% 0.35/0.64 % sh5l with pid 1722560 completed with status 0
% 0.35/0.64 % Result found by sh5l
% 0.35/0.64 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.35/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.35/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.35/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.35/0.64 % Starting sh5l with 300s (1) cores
% 0.35/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.35/0.64 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.35/0.64 % Search class: FUUPM-FFSF22-MFFFFFNN
% 0.35/0.64 % Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 0.35/0.64 % Starting SubtermCWHack with 28s (1) cores
% 0.35/0.64 % SubtermCWHack with pid 1722568 completed with status 0
% 0.35/0.64 % Result found by SubtermCWHack
% 0.35/0.65 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.35/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.65 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.35/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.35/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.35/0.65 % Starting sh5l with 300s (1) cores
% 0.35/0.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.35/0.65 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.35/0.65 % Search class: FUUPM-FFSF22-MFFFFFNN
% 0.35/0.65 % Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 0.35/0.65 % Starting SubtermCWHack with 28s (1) cores
% 0.35/0.65 % Preprocessing time : 0.001 s
% 0.35/0.65
% 0.35/0.65 % Proof found!
% 0.35/0.65 % SZS status Unsatisfiable
% 0.35/0.65 % SZS output start CNFRefutation
% See solution above
% 0.35/0.65 % Parsed axioms : 8
% 0.35/0.65 % Removed by relevancy pruning/SinE : 0
% 0.35/0.65 % Initial clauses : 8
% 0.35/0.65 % Removed in clause preprocessing : 0
% 0.35/0.65 % Initial clauses in saturation : 8
% 0.35/0.65 % Processed clauses : 163
% 0.35/0.65 % ...of these trivial : 51
% 0.35/0.65 % ...subsumed : 0
% 0.35/0.65 % ...remaining for further processing : 112
% 0.35/0.65 % Other redundant clauses eliminated : 0
% 0.35/0.65 % Clauses deleted for lack of memory : 0
% 0.35/0.65 % Backward-subsumed : 0
% 0.35/0.65 % Backward-rewritten : 78
% 0.35/0.65 % Generated clauses : 2577
% 0.35/0.65 % ...of the previous two non-redundant : 1748
% 0.35/0.65 % ...aggressively subsumed : 0
% 0.35/0.65 % Contextual simplify-reflections : 0
% 0.35/0.65 % Paramodulations : 2577
% 0.35/0.65 % Factorizations : 0
% 0.35/0.65 % NegExts : 0
% 0.35/0.65 % Equation resolutions : 0
% 0.35/0.65 % Disequality decompositions : 0
% 0.35/0.65 % Total rewrite steps : 2994
% 0.35/0.65 % ...of those cached : 2269
% 0.35/0.65 % Propositional unsat checks : 0
% 0.35/0.65 % Propositional check models : 0
% 0.35/0.65 % Propositional check unsatisfiable : 0
% 0.35/0.65 % Propositional clauses : 0
% 0.35/0.65 % Propositional clauses after purity: 0
% 0.35/0.65 % Propositional unsat core size : 0
% 0.35/0.65 % Propositional preprocessing time : 0.000
% 0.35/0.65 % Propositional encoding time : 0.000
% 0.35/0.65 % Propositional solver time : 0.000
% 0.35/0.65 % Success case prop preproc time : 0.000
% 0.35/0.65 % Success case prop encoding time : 0.000
% 0.35/0.65 % Success case prop solver time : 0.000
% 0.35/0.65 % Current number of processed clauses : 34
% 0.35/0.65 % Positive orientable unit clauses : 34
% 0.35/0.65 % Positive unorientable unit clauses: 0
% 0.35/0.65 % Negative unit clauses : 0
% 0.35/0.65 % Non-unit-clauses : 0
% 0.35/0.65 % Current number of unprocessed clauses: 1559
% 0.35/0.65 % ...number of literals in the above : 1559
% 0.35/0.65 % Current number of archived formulas : 0
% 0.35/0.65 % Current number of archived clauses : 78
% 0.35/0.65 % Clause-clause subsumption calls (NU) : 0
% 0.35/0.65 % Rec. Clause-clause subsumption calls : 0
% 0.35/0.65 % Non-unit clause-clause subsumptions : 0
% 0.35/0.65 % Unit Clause-clause subsumption calls : 1
% 0.35/0.65 % Rewrite failures with RHS unbound : 6
% 0.35/0.65 % BW rewrite match attempts : 236
% 0.35/0.65 % BW rewrite match successes : 84
% 0.35/0.65 % Condensation attempts : 0
% 0.35/0.65 % Condensation successes : 0
% 0.35/0.65 % Termbank termtop insertions : 31516
% 0.35/0.65 % Search garbage collected termcells : 2
% 0.35/0.65
% 0.35/0.65 % -------------------------------------------------
% 0.35/0.65 % User time : 0.039 s
% 0.35/0.65 % System time : 0.002 s
% 0.35/0.65 % Total time : 0.041 s
% 0.35/0.65 % Maximum resident set size: 3632 pages
% 0.35/0.65
% 0.35/0.65 % -------------------------------------------------
% 0.35/0.65 % User time : 0.043 s
% 0.35/0.65 % System time : 0.007 s
% 0.35/0.65 % Total time : 0.050 s
% 0.35/0.65 % Maximum resident set size: 4864 pages
% 0.35/0.65 % E exiting
%------------------------------------------------------------------------------