%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP777-10 : 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 : n012.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 12:41:14 PM UTC 2026
% Result : Unsatisfiable 1.32s 0.65s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 57 ( 57 unt; 0 nHn; 11 RR)
% Number of literals : 57 ( 56 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 106 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos08,axiom,
bigC(X1,X2,X3) = product(product(X1,X2),product(X3,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
cnf(sos06,axiom,
product(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
cnf(sos05,axiom,
product(product(X1,X2),product(X3,X4)) = product(product(X1,X3),product(X2,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
cnf(sos02,axiom,
product(X1,difference(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
cnf(sos01,axiom,
difference(X1,product(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
cnf(sos04,axiom,
product(quotient(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
cnf(sos07,axiom,
product(product(product(X1,X2),X2),product(X2,product(X2,X1))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
cnf(sos03,axiom,
quotient(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
cnf(sos09,axiom,
product(product(a,c),product(c,b)) = product(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
cnf(goal,negated_conjecture,
bigC(a,b,x0) != bigC(c,c,x0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c_0_10,axiom,
bigC(X1,X2,X3) = product(product(X1,X2),product(X3,X1)),
sos08 ).
cnf(c_0_11,axiom,
product(X1,X1) = X1,
sos06 ).
cnf(c_0_12,axiom,
product(product(X1,X2),product(X3,X4)) = product(product(X1,X3),product(X2,X4)),
sos05 ).
cnf(c_0_13,plain,
bigC(X1,X2,X1) = product(product(X1,X2),X1),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
bigC(X1,X2,X3) = bigC(X1,X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_12]),c_0_10]) ).
cnf(c_0_15,plain,
bigC(X1,X1,X2) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
product(product(X1,X2),X1) = product(X1,product(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_17,axiom,
product(X1,difference(X1,X2)) = X2,
sos02 ).
cnf(c_0_18,axiom,
difference(X1,product(X1,X2)) = X2,
sos01 ).
cnf(c_0_19,plain,
product(X1,product(difference(X1,X2),X1)) = product(X2,X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
difference(X1,product(X2,X1)) = product(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
product(quotient(X1,X2),X2) = X1,
sos04 ).
cnf(c_0_22,axiom,
product(product(product(X1,X2),X2),product(X2,product(X2,X1))) = X2,
sos07 ).
cnf(c_0_23,plain,
product(difference(X1,quotient(X2,X1)),X1) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
bigC(X1,difference(X1,X2),X3) = product(X2,product(X3,X1)),
inference(spm,[status(thm)],[c_0_10,c_0_17]) ).
cnf(c_0_25,axiom,
quotient(product(X1,X2),X2) = X1,
sos03 ).
cnf(c_0_26,plain,
product(product(X1,X2),product(X3,X2)) = product(product(X1,X3),X2),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_27,plain,
product(product(difference(X1,X2),X1),product(X1,quotient(X2,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_17]) ).
cnf(c_0_28,plain,
bigC(X1,X2,difference(X1,X3)) = product(X3,product(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_24]) ).
cnf(c_0_29,plain,
quotient(product(X1,product(X2,X1)),X1) = product(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_30,plain,
difference(product(product(X1,X2),X2),X2) = product(X2,product(X2,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_31,axiom,
product(product(a,c),product(c,b)) = product(a,b),
sos09 ).
cnf(c_0_32,plain,
quotient(product(product(X1,X2),X3),product(X2,X3)) = product(X1,X3),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
product(product(difference(X1,X2),X1),X2) = product(X2,X1),
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_16,c_0_27]),c_0_19]),c_0_10]),c_0_28]),c_0_21]),c_0_11]) ).
cnf(c_0_34,plain,
quotient(product(X1,X2),X1) = product(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_35,plain,
product(X1,product(X1,quotient(X2,X1))) = difference(product(X2,X1),X1),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_36,plain,
quotient(product(a,b),product(c,b)) = product(a,c),
inference(spm,[status(thm)],[c_0_25,c_0_31]) ).
cnf(c_0_37,plain,
quotient(product(X1,X2),product(X3,X2)) = product(quotient(X1,X3),X2),
inference(spm,[status(thm)],[c_0_32,c_0_21]) ).
cnf(c_0_38,plain,
product(difference(X1,X2),quotient(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_23]),c_0_21]) ).
cnf(c_0_39,plain,
quotient(difference(product(X1,X2),X2),X2) = difference(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_34]),c_0_35]),c_0_21]) ).
cnf(c_0_40,plain,
product(product(quotient(X1,X2),X3),X2) = product(X1,product(X3,X2)),
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
cnf(c_0_41,plain,
product(quotient(a,c),b) = product(a,c),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
product(product(X1,X2),product(X1,X3)) = product(X1,product(X2,X3)),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_43,plain,
difference(difference(X1,X2),X2) = quotient(X2,X1),
inference(spm,[status(thm)],[c_0_18,c_0_38]) ).
cnf(c_0_44,plain,
difference(product(X1,X2),X2) = product(difference(X1,X2),X2),
inference(spm,[status(thm)],[c_0_21,c_0_39]) ).
cnf(c_0_45,plain,
difference(quotient(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_46,negated_conjecture,
bigC(a,b,x0) != bigC(c,c,x0),
inference(fof_simplification,[status(thm)],[goal]) ).
cnf(c_0_47,plain,
product(product(a,c),c) = product(a,product(b,c)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
quotient(product(X1,product(X2,X3)),product(X1,X3)) = product(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_42]) ).
cnf(c_0_49,plain,
quotient(X1,product(X2,X1)) = product(quotient(X1,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_44]),c_0_43]) ).
cnf(c_0_50,plain,
product(product(X1,quotient(X2,X1)),X2) = product(X2,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_33,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
bigC(a,b,x0) != bigC(c,c,x0),
c_0_46 ).
cnf(c_0_52,plain,
product(product(X1,quotient(X2,X3)),product(X4,X3)) = product(product(X1,X4),X2),
inference(spm,[status(thm)],[c_0_12,c_0_21]) ).
cnf(c_0_53,plain,
product(c,quotient(c,a)) = product(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_47]),c_0_48]),c_0_49]),c_0_26]),c_0_50]) ).
cnf(c_0_54,negated_conjecture,
bigC(a,b,x0) != product(c,product(x0,c)),
inference(rw,[status(thm)],[c_0_51,c_0_15]) ).
cnf(c_0_55,plain,
bigC(a,b,X1) = product(c,product(X1,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_10]),c_0_16]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP777-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n012.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:39:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.41 Running first-order theorem proving
% 0.04/0.41 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
% 1.32/0.65 % Version: 3.5.1
% 1.32/0.65 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.32/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.32/0.65 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.32/0.65 % Starting new_bool_3 with 300s (1) cores
% 1.32/0.65 % Starting new_bool_1 with 300s (1) cores
% 1.32/0.65 % Starting sh5l with 300s (1) cores
% 1.32/0.65 % sh5l with pid 825297 completed with status 0
% 1.32/0.65 % Result found by sh5l
% 1.32/0.65 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.32/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.32/0.65 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.32/0.65 % Starting new_bool_3 with 300s (1) cores
% 1.32/0.65 % Starting new_bool_1 with 300s (1) cores
% 1.32/0.65 % Starting sh5l with 300s (1) cores
% 1.32/0.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 1.32/0.65 % SinE strategy is gf500_gu_R04_F100_L20000
% 1.32/0.65 % Search class: FUUPM-FFSF32-MFFFFFNN
% 1.32/0.65 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.32/0.65 % Starting SubtermCWHack with 28s (1) cores
% 1.32/0.65 % SubtermCWHack with pid 825305 completed with status 0
% 1.32/0.65 % Result found by SubtermCWHack
% 1.32/0.65 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.32/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.32/0.65 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.32/0.65 % Starting new_bool_3 with 300s (1) cores
% 1.32/0.65 % Starting new_bool_1 with 300s (1) cores
% 1.32/0.65 % Starting sh5l with 300s (1) cores
% 1.32/0.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 1.32/0.65 % SinE strategy is gf500_gu_R04_F100_L20000
% 1.32/0.65 % Search class: FUUPM-FFSF32-MFFFFFNN
% 1.32/0.65 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.32/0.65 % Starting SubtermCWHack with 28s (1) cores
% 1.32/0.65 % Preprocessing time : 0.001 s
% 1.32/0.65
% 1.32/0.65 % Proof found!
% 1.32/0.65 % SZS status Unsatisfiable
% 1.32/0.65 % SZS output start CNFRefutation
% See solution above
% 1.32/0.65 % Parsed axioms : 10
% 1.32/0.65 % Removed by relevancy pruning/SinE : 0
% 1.32/0.65 % Initial clauses : 10
% 1.32/0.65 % Removed in clause preprocessing : 0
% 1.32/0.65 % Initial clauses in saturation : 10
% 1.32/0.65 % Processed clauses : 565
% 1.32/0.65 % ...of these trivial : 253
% 1.32/0.65 % ...subsumed : 52
% 1.32/0.65 % ...remaining for further processing : 260
% 1.32/0.65 % Other redundant clauses eliminated : 0
% 1.32/0.65 % Clauses deleted for lack of memory : 0
% 1.32/0.65 % Backward-subsumed : 0
% 1.32/0.65 % Backward-rewritten : 46
% 1.32/0.65 % Generated clauses : 18257
% 1.32/0.65 % ...of the previous two non-redundant : 16563
% 1.32/0.65 % ...aggressively subsumed : 0
% 1.32/0.65 % Contextual simplify-reflections : 0
% 1.32/0.65 % Paramodulations : 18257
% 1.32/0.65 % Factorizations : 0
% 1.32/0.65 % NegExts : 0
% 1.32/0.65 % Equation resolutions : 0
% 1.32/0.65 % Disequality decompositions : 0
% 1.32/0.65 % Total rewrite steps : 10972
% 1.32/0.65 % ...of those cached : 9266
% 1.32/0.65 % Propositional unsat checks : 0
% 1.32/0.65 % Propositional check models : 0
% 1.32/0.65 % Propositional check unsatisfiable : 0
% 1.32/0.65 % Propositional clauses : 0
% 1.32/0.65 % Propositional clauses after purity: 0
% 1.32/0.65 % Propositional unsat core size : 0
% 1.32/0.65 % Propositional preprocessing time : 0.000
% 1.32/0.65 % Propositional encoding time : 0.000
% 1.32/0.65 % Propositional solver time : 0.000
% 1.32/0.65 % Success case prop preproc time : 0.000
% 1.32/0.65 % Success case prop encoding time : 0.000
% 1.32/0.65 % Success case prop solver time : 0.000
% 1.32/0.65 % Current number of processed clauses : 214
% 1.32/0.65 % Positive orientable unit clauses : 207
% 1.32/0.65 % Positive unorientable unit clauses: 7
% 1.32/0.65 % Negative unit clauses : 0
% 1.32/0.65 % Non-unit-clauses : 0
% 1.32/0.65 % Current number of unprocessed clauses: 15896
% 1.32/0.65 % ...number of literals in the above : 15896
% 1.32/0.65 % Current number of archived formulas : 0
% 1.32/0.65 % Current number of archived clauses : 46
% 1.32/0.65 % Clause-clause subsumption calls (NU) : 0
% 1.32/0.65 % Rec. Clause-clause subsumption calls : 0
% 1.32/0.65 % Non-unit clause-clause subsumptions : 0
% 1.32/0.65 % Unit Clause-clause subsumption calls : 4
% 1.32/0.65 % Rewrite failures with RHS unbound : 0
% 1.32/0.65 % BW rewrite match attempts : 419
% 1.32/0.65 % BW rewrite match successes : 59
% 1.32/0.65 % Condensation attempts : 0
% 1.32/0.65 % Condensation successes : 0
% 1.32/0.65 % Termbank termtop insertions : 222276
% 1.32/0.65 % Search garbage collected termcells : 2
% 1.32/0.65
% 1.32/0.65 % -------------------------------------------------
% 1.32/0.65 % User time : 0.169 s
% 1.32/0.65 % System time : 0.020 s
% 1.32/0.65 % Total time : 0.189 s
% 1.32/0.65 % Maximum resident set size: 3580 pages
% 1.32/0.65
% 1.32/0.65 % -------------------------------------------------
% 1.32/0.65 % User time : 0.169 s
% 1.32/0.65 % System time : 0.025 s
% 1.32/0.65 % Total time : 0.194 s
% 1.32/0.65 % Maximum resident set size: 4864 pages
% 1.32/0.65 % E exiting
%------------------------------------------------------------------------------