%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP767-1 : TPTP v9.3.1. Released v4.1.0.
% 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 12:41:13 PM UTC 2026
% Result : Unsatisfiable 2.94s 0.98s
% Output : CNFRefutation 2.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of clauses : 69 ( 69 unt; 0 nHn; 4 RR)
% Number of literals : 69 ( 68 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 110 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos03,axiom,
product(X1,difference(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
cnf(sos07,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
cnf(sos06,axiom,
product(quotient(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
cnf(sos10,axiom,
j(X1) = quotient(one,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).
cnf(sos11,axiom,
product(i(X1),X1) = product(X1,j(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos11) ).
cnf(sos12,axiom,
eta(X1) = product(i(X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).
cnf(sos09,axiom,
i(X1) = difference(X1,one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
cnf(sos04,axiom,
difference(X1,product(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
cnf(sos14,axiom,
product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos14) ).
cnf(sos01,axiom,
product(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
cnf(sos13,axiom,
product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos13) ).
cnf(sos05,axiom,
quotient(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
cnf(sos16,axiom,
product(eta(X1),product(X2,X3)) = product(product(eta(X1),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos16) ).
cnf(sos02,axiom,
product(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
cnf(sos15,axiom,
product(X1,product(X2,eta(X1))) = product(product(X1,X2),eta(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos15) ).
cnf(sos08,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
cnf(goals,negated_conjecture,
product(j(j(x0)),j(product(x1,x0))) != j(x1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_17,axiom,
product(X1,difference(X1,X2)) = X2,
sos03 ).
cnf(c_0_18,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
sos07 ).
cnf(c_0_19,axiom,
product(quotient(X1,X2),X2) = X1,
sos06 ).
cnf(c_0_20,axiom,
j(X1) = quotient(one,X1),
sos10 ).
cnf(c_0_21,axiom,
product(i(X1),X1) = product(X1,j(X1)),
sos11 ).
cnf(c_0_22,axiom,
eta(X1) = product(i(X1),X1),
sos12 ).
cnf(c_0_23,plain,
product(X1,quotient(product(X2,product(X3,X1)),X1)) = product(product(X1,X2),X3),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
product(j(X1),X1) = one,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
product(X1,j(X1)) = eta(X1),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
i(X1) = difference(X1,one),
sos09 ).
cnf(c_0_27,axiom,
difference(X1,product(X1,X2)) = X2,
sos04 ).
cnf(c_0_28,plain,
product(product(X1,j(product(X2,X1))),X2) = eta(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20]),c_0_25]) ).
cnf(c_0_29,axiom,
product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2),
sos14 ).
cnf(c_0_30,plain,
product(X1,i(X1)) = one,
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_31,axiom,
product(X1,one) = X1,
sos01 ).
cnf(c_0_32,axiom,
product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
sos13 ).
cnf(c_0_33,axiom,
quotient(product(X1,X2),X2) = X1,
sos05 ).
cnf(c_0_34,plain,
difference(product(X1,j(product(X2,X1))),eta(X1)) = X2,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,axiom,
product(eta(X1),product(X2,X3)) = product(product(eta(X1),X2),X3),
sos16 ).
cnf(c_0_36,plain,
product(j(j(X1)),i(eta(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_37,plain,
eta(i(X1)) = eta(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_32]),c_0_30]),c_0_31]) ).
cnf(c_0_38,plain,
j(i(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_30]),c_0_20]) ).
cnf(c_0_39,plain,
i(j(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_24]),c_0_26]) ).
cnf(c_0_40,plain,
product(X1,eta(X1)) = j(j(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_31]),c_0_31]) ).
cnf(c_0_41,axiom,
product(one,X1) = X1,
sos02 ).
cnf(c_0_42,plain,
difference(product(X1,j(X2)),eta(X1)) = quotient(X2,X1),
inference(spm,[status(thm)],[c_0_34,c_0_19]) ).
cnf(c_0_43,plain,
difference(product(eta(X1),X2),product(eta(X1),product(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_27,c_0_35]) ).
cnf(c_0_44,axiom,
product(X1,product(X2,eta(X1))) = product(product(X1,X2),eta(X1)),
sos15 ).
cnf(c_0_45,plain,
product(j(X1),i(eta(X1))) = i(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_46,plain,
eta(j(X1)) = eta(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_39]),c_0_25]) ).
cnf(c_0_47,plain,
product(i(X1),eta(X1)) = j(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_37]),c_0_38]) ).
cnf(c_0_48,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
sos08 ).
cnf(c_0_49,plain,
quotient(product(i(X1),product(X2,X1)),X1) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_30]),c_0_41]) ).
cnf(c_0_50,plain,
difference(product(X1,X2),eta(X1)) = quotient(i(X2),X1),
inference(spm,[status(thm)],[c_0_42,c_0_38]) ).
cnf(c_0_51,plain,
difference(product(eta(X1),X2),eta(X1)) = i(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_30]),c_0_31]) ).
cnf(c_0_52,plain,
product(j(X1),eta(eta(X1))) = j(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47]),c_0_46]),c_0_22]) ).
cnf(c_0_53,plain,
difference(X1,X1) = one,
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_54,plain,
quotient(difference(X1,X2),X2) = difference(product(X2,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_30]),c_0_31]) ).
cnf(c_0_55,plain,
quotient(i(X1),i(i(X2))) = i(product(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_32]),c_0_37]),c_0_37]),c_0_51]) ).
cnf(c_0_56,plain,
difference(X1,eta(X1)) = j(X1),
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_57,plain,
eta(eta(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_52]),c_0_53]) ).
cnf(c_0_58,plain,
product(difference(product(X1,X2),X1),X1) = difference(X2,X1),
inference(spm,[status(thm)],[c_0_19,c_0_54]) ).
cnf(c_0_59,plain,
product(i(product(X1,X2)),i(i(X1))) = i(X2),
inference(spm,[status(thm)],[c_0_19,c_0_55]) ).
cnf(c_0_60,plain,
product(eta(X1),product(j(j(X1)),X2)) = product(X1,X2),
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_32,c_0_29]),c_0_38]),c_0_38]),c_0_37]),c_0_37]),c_0_29]) ).
cnf(c_0_61,plain,
i(eta(X1)) = j(eta(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_26]) ).
cnf(c_0_62,plain,
product(i(X1),eta(X2)) = difference(X1,eta(X2)),
inference(spm,[status(thm)],[c_0_58,c_0_51]) ).
cnf(c_0_63,plain,
i(product(j(j(X1)),X2)) = quotient(i(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),c_0_39]),c_0_62]),c_0_50]) ).
cnf(c_0_64,negated_conjecture,
product(j(j(x0)),j(product(x1,x0))) != j(x1),
inference(fof_simplification,[status(thm)],[goals]) ).
cnf(c_0_65,plain,
j(quotient(i(X1),X2)) = product(j(j(X2)),X1),
inference(spm,[status(thm)],[c_0_38,c_0_63]) ).
cnf(c_0_66,negated_conjecture,
product(j(j(x0)),j(product(x1,x0))) != j(x1),
c_0_64 ).
cnf(c_0_67,plain,
product(j(j(X1)),j(X2)) = j(quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_65,c_0_39]) ).
cnf(c_0_68,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP767-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:39:11 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 2.94/0.98 % Version: 3.5.1
% 2.94/0.98 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.94/0.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.94/0.98 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.94/0.98 % Starting new_bool_3 with 300s (1) cores
% 2.94/0.98 % Starting new_bool_1 with 300s (1) cores
% 2.94/0.98 % Starting sh5l with 300s (1) cores
% 2.94/0.98 % new_bool_3 with pid 140643 completed with status 0
% 2.94/0.98 % Result found by new_bool_3
% 2.94/0.98 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.94/0.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.94/0.98 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.94/0.98 % Starting new_bool_3 with 300s (1) cores
% 2.94/0.98 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.94/0.98 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.94/0.98 % Search class: FUUPM-FFSF21-MFFFFFNN
% 2.94/0.98 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 2.94/0.98 % Starting SubtermCWHack with 28s (1) cores
% 2.94/0.98 % SubtermCWHack with pid 140648 completed with status 0
% 2.94/0.98 % Result found by SubtermCWHack
% 2.94/0.98 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.94/0.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.94/0.98 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.94/0.98 % Starting new_bool_3 with 300s (1) cores
% 2.94/0.98 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.94/0.98 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.94/0.98 % Search class: FUUPM-FFSF21-MFFFFFNN
% 2.94/0.98 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 2.94/0.98 % Starting SubtermCWHack with 28s (1) cores
% 2.94/0.98 % Preprocessing time : 0.002 s
% 2.94/0.98
% 2.94/0.98 % Proof found!
% 2.94/0.98 % SZS status Unsatisfiable
% 2.94/0.98 % SZS output start CNFRefutation
% See solution above
% 2.94/0.98 % Parsed axioms : 21
% 2.94/0.98 % Removed by relevancy pruning/SinE : 4
% 2.94/0.98 % Initial clauses : 17
% 2.94/0.98 % Removed in clause preprocessing : 0
% 2.94/0.98 % Initial clauses in saturation : 17
% 2.94/0.98 % Processed clauses : 1412
% 2.94/0.98 % ...of these trivial : 491
% 2.94/0.98 % ...subsumed : 416
% 2.94/0.98 % ...remaining for further processing : 505
% 2.94/0.98 % Other redundant clauses eliminated : 0
% 2.94/0.98 % Clauses deleted for lack of memory : 0
% 2.94/0.98 % Backward-subsumed : 0
% 2.94/0.98 % Backward-rewritten : 185
% 2.94/0.98 % Generated clauses : 43800
% 2.94/0.98 % ...of the previous two non-redundant : 27909
% 2.94/0.98 % ...aggressively subsumed : 0
% 2.94/0.98 % Contextual simplify-reflections : 0
% 2.94/0.98 % Paramodulations : 43800
% 2.94/0.98 % Factorizations : 0
% 2.94/0.98 % NegExts : 0
% 2.94/0.98 % Equation resolutions : 0
% 2.94/0.98 % Disequality decompositions : 0
% 2.94/0.98 % Total rewrite steps : 93302
% 2.94/0.98 % ...of those cached : 83434
% 2.94/0.98 % Propositional unsat checks : 0
% 2.94/0.98 % Propositional check models : 0
% 2.94/0.98 % Propositional check unsatisfiable : 0
% 2.94/0.98 % Propositional clauses : 0
% 2.94/0.98 % Propositional clauses after purity: 0
% 2.94/0.98 % Propositional unsat core size : 0
% 2.94/0.98 % Propositional preprocessing time : 0.000
% 2.94/0.98 % Propositional encoding time : 0.000
% 2.94/0.98 % Propositional solver time : 0.000
% 2.94/0.98 % Success case prop preproc time : 0.000
% 2.94/0.98 % Success case prop encoding time : 0.000
% 2.94/0.98 % Success case prop solver time : 0.000
% 2.94/0.98 % Current number of processed clauses : 320
% 2.94/0.98 % Positive orientable unit clauses : 305
% 2.94/0.98 % Positive unorientable unit clauses: 15
% 2.94/0.98 % Negative unit clauses : 0
% 2.94/0.98 % Non-unit-clauses : 0
% 2.94/0.98 % Current number of unprocessed clauses: 26151
% 2.94/0.98 % ...number of literals in the above : 26151
% 2.94/0.98 % Current number of archived formulas : 0
% 2.94/0.98 % Current number of archived clauses : 185
% 2.94/0.98 % Clause-clause subsumption calls (NU) : 0
% 2.94/0.98 % Rec. Clause-clause subsumption calls : 0
% 2.94/0.98 % Non-unit clause-clause subsumptions : 0
% 2.94/0.98 % Unit Clause-clause subsumption calls : 23
% 2.94/0.98 % Rewrite failures with RHS unbound : 0
% 2.94/0.98 % BW rewrite match attempts : 810
% 2.94/0.98 % BW rewrite match successes : 190
% 2.94/0.98 % Condensation attempts : 0
% 2.94/0.98 % Condensation successes : 0
% 2.94/0.98 % Termbank termtop insertions : 594404
% 2.94/0.98 % Search garbage collected termcells : 17
% 2.94/0.98
% 2.94/0.98 % -------------------------------------------------
% 2.94/0.98 % User time : 0.409 s
% 2.94/0.98 % System time : 0.030 s
% 2.94/0.98 % Total time : 0.439 s
% 2.94/0.98 % Maximum resident set size: 3644 pages
% 2.94/0.98
% 2.94/0.98 % -------------------------------------------------
% 2.94/0.98 % User time : 0.410 s
% 2.94/0.98 % System time : 0.037 s
% 2.94/0.98 % Total time : 0.447 s
% 2.94/0.98 % Maximum resident set size: 4864 pages
% 2.94/0.98 % E exiting
%------------------------------------------------------------------------------