%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP186-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:42:50 PM UTC 2026
% Result : Unsatisfiable 26.02s 4.26s
% Output : CNFRefutation 26.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of clauses : 62 ( 62 unt; 0 nHn; 7 RR)
% Number of literals : 62 ( 61 equ; 4 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 116 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(lub_absorbtion,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
cnf(p23_3,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_3) ).
cnf(p23_1,hypothesis,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_1) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
cnf(p23_2,hypothesis,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_2) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
cnf(monotony_glb1,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(prove_p23,negated_conjecture,
least_upper_bound(multiply(a,b),identity) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p23) ).
cnf(monotony_lub1,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
cnf(c_0_16,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_17,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_18,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
p23_3 ).
cnf(c_0_19,hypothesis,
inverse(identity) = identity,
p23_1 ).
cnf(c_0_20,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_21,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
associativity_of_glb ).
cnf(c_0_23,hypothesis,
multiply(inverse(X1),identity) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_24,hypothesis,
inverse(inverse(X1)) = X1,
p23_2 ).
cnf(c_0_25,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_27,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_28,hypothesis,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_30,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_31,plain,
greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3),
inference(spm,[status(thm)],[c_0_22,c_0_26]) ).
cnf(c_0_32,axiom,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
associativity_of_lub ).
cnf(c_0_33,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_34,hypothesis,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_17]) ).
cnf(c_0_35,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_36,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
cnf(c_0_37,plain,
least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(X1,X3))) = least_upper_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_38,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_20]),c_0_29]) ).
cnf(c_0_39,hypothesis,
multiply(inverse(X1),greatest_lower_bound(X1,identity)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_17]) ).
cnf(c_0_40,plain,
greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X2,greatest_lower_bound(X1,X3))) = least_upper_bound(X2,greatest_lower_bound(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_17]) ).
cnf(c_0_41,hypothesis,
least_upper_bound(greatest_lower_bound(X1,identity),greatest_lower_bound(identity,inverse(X1))) = multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(X1,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_29]) ).
cnf(c_0_42,hypothesis,
greatest_lower_bound(X1,multiply(least_upper_bound(X1,X2),greatest_lower_bound(X3,identity))) = greatest_lower_bound(X1,multiply(least_upper_bound(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_31,c_0_34]) ).
cnf(c_0_43,plain,
multiply(least_upper_bound(X1,inverse(X2)),X2) = least_upper_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_35]),c_0_29]) ).
cnf(c_0_44,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_45,hypothesis,
multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(X1,identity)) = identity,
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_40,c_0_41]),c_0_21]),c_0_42]),c_0_43]),c_0_20]),c_0_26]) ).
cnf(c_0_46,hypothesis,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_35,c_0_24]) ).
cnf(c_0_47,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_35]),c_0_20]) ).
cnf(c_0_48,hypothesis,
multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,inverse(X1))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_24]),c_0_17]) ).
cnf(c_0_49,hypothesis,
least_upper_bound(identity,multiply(X1,inverse(X2))) = multiply(least_upper_bound(X2,X1),inverse(X2)),
inference(spm,[status(thm)],[c_0_33,c_0_46]) ).
cnf(c_0_50,hypothesis,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_51,plain,
multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3),
inference(spm,[status(thm)],[c_0_27,c_0_47]) ).
cnf(c_0_52,hypothesis,
multiply(least_upper_bound(X1,X2),greatest_lower_bound(inverse(X1),inverse(X2))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_44]),c_0_51]),c_0_28]) ).
cnf(c_0_53,negated_conjecture,
least_upper_bound(multiply(a,b),identity) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(fof_simplification,[status(thm)],[prove_p23]) ).
cnf(c_0_54,hypothesis,
greatest_lower_bound(inverse(X1),inverse(X2)) = inverse(least_upper_bound(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_52]),c_0_28]) ).
cnf(c_0_55,negated_conjecture,
least_upper_bound(multiply(a,b),identity) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
c_0_53 ).
cnf(c_0_56,hypothesis,
inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(X1,inverse(X2)),
inference(spm,[status(thm)],[c_0_54,c_0_24]) ).
cnf(c_0_57,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_58,negated_conjecture,
multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) != least_upper_bound(identity,multiply(a,b)),
inference(rw,[status(thm)],[c_0_55,c_0_29]) ).
cnf(c_0_59,hypothesis,
inverse(greatest_lower_bound(X1,inverse(X2))) = least_upper_bound(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_24,c_0_56]) ).
cnf(c_0_60,hypothesis,
multiply(X1,least_upper_bound(X2,inverse(X1))) = least_upper_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_46]),c_0_29]) ).
cnf(c_0_61,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59]),c_0_29]),c_0_60])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP186-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 20 20:06:11 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 26.02/4.26 % Version: 3.5.1
% 26.02/4.26 % Preprocessing class: FSMSSMSSSSSNFFN.
% 26.02/4.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 26.02/4.26 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 26.02/4.26 % Starting new_bool_3 with 300s (1) cores
% 26.02/4.26 % Starting new_bool_1 with 300s (1) cores
% 26.02/4.26 % Starting sh5l with 300s (1) cores
% 26.02/4.26 % sh5l with pid 3490987 completed with status 0
% 26.02/4.26 % Result found by sh5l
% 26.02/4.26 % Preprocessing class: FSMSSMSSSSSNFFN.
% 26.02/4.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 26.02/4.26 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 26.02/4.26 % Starting new_bool_3 with 300s (1) cores
% 26.02/4.26 % Starting new_bool_1 with 300s (1) cores
% 26.02/4.26 % Starting sh5l with 300s (1) cores
% 26.02/4.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 26.02/4.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 26.02/4.26 % Search class: FUUPM-FFSF21-MFFFFFNN
% 26.02/4.26 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 26.02/4.26 % Starting SubtermCWHack with 28s (1) cores
% 26.02/4.26 % SubtermCWHack with pid 3490989 completed with status 0
% 26.02/4.26 % Result found by SubtermCWHack
% 26.02/4.26 % Preprocessing class: FSMSSMSSSSSNFFN.
% 26.02/4.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 26.02/4.26 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 26.02/4.26 % Starting new_bool_3 with 300s (1) cores
% 26.02/4.26 % Starting new_bool_1 with 300s (1) cores
% 26.02/4.26 % Starting sh5l with 300s (1) cores
% 26.02/4.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 26.02/4.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 26.02/4.26 % Search class: FUUPM-FFSF21-MFFFFFNN
% 26.02/4.26 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 26.02/4.26 % Starting SubtermCWHack with 28s (1) cores
% 26.02/4.26 % Preprocessing time : 0.001 s
% 26.02/4.26
% 26.02/4.26 % Proof found!
% 26.02/4.26 % SZS status Unsatisfiable
% 26.02/4.26 % SZS output start CNFRefutation
% See solution above
% 26.02/4.26 % Parsed axioms : 19
% 26.02/4.26 % Removed by relevancy pruning/SinE : 0
% 26.02/4.26 % Initial clauses : 19
% 26.02/4.26 % Removed in clause preprocessing : 0
% 26.02/4.26 % Initial clauses in saturation : 19
% 26.02/4.26 % Processed clauses : 15187
% 26.02/4.26 % ...of these trivial : 5503
% 26.02/4.26 % ...subsumed : 8644
% 26.02/4.26 % ...remaining for further processing : 1040
% 26.02/4.26 % Other redundant clauses eliminated : 0
% 26.02/4.26 % Clauses deleted for lack of memory : 0
% 26.02/4.26 % Backward-subsumed : 0
% 26.02/4.26 % Backward-rewritten : 193
% 26.02/4.26 % Generated clauses : 516027
% 26.02/4.26 % ...of the previous two non-redundant : 332124
% 26.02/4.26 % ...aggressively subsumed : 0
% 26.02/4.26 % Contextual simplify-reflections : 0
% 26.02/4.26 % Paramodulations : 516027
% 26.02/4.26 % Factorizations : 0
% 26.02/4.26 % NegExts : 0
% 26.02/4.26 % Equation resolutions : 0
% 26.02/4.26 % Disequality decompositions : 0
% 26.02/4.26 % Total rewrite steps : 693377
% 26.02/4.26 % ...of those cached : 544209
% 26.02/4.26 % Propositional unsat checks : 0
% 26.02/4.26 % Propositional check models : 0
% 26.02/4.26 % Propositional check unsatisfiable : 0
% 26.02/4.26 % Propositional clauses : 0
% 26.02/4.26 % Propositional clauses after purity: 0
% 26.02/4.26 % Propositional unsat core size : 0
% 26.02/4.26 % Propositional preprocessing time : 0.000
% 26.02/4.26 % Propositional encoding time : 0.000
% 26.02/4.26 % Propositional solver time : 0.000
% 26.02/4.27 % Success case prop preproc time : 0.000
% 26.02/4.27 % Success case prop encoding time : 0.000
% 26.02/4.27 % Success case prop solver time : 0.000
% 26.02/4.27 % Current number of processed clauses : 847
% 26.02/4.27 % Positive orientable unit clauses : 804
% 26.02/4.27 % Positive unorientable unit clauses: 43
% 26.02/4.27 % Negative unit clauses : 0
% 26.02/4.27 % Non-unit-clauses : 0
% 26.02/4.27 % Current number of unprocessed clauses: 316059
% 26.02/4.27 % ...number of literals in the above : 316059
% 26.02/4.27 % Current number of archived formulas : 0
% 26.02/4.27 % Current number of archived clauses : 193
% 26.02/4.27 % Clause-clause subsumption calls (NU) : 0
% 26.02/4.27 % Rec. Clause-clause subsumption calls : 0
% 26.02/4.27 % Non-unit clause-clause subsumptions : 0
% 26.02/4.27 % Unit Clause-clause subsumption calls : 216
% 26.02/4.27 % Rewrite failures with RHS unbound : 0
% 26.02/4.27 % BW rewrite match attempts : 7583
% 26.02/4.27 % BW rewrite match successes : 530
% 26.02/4.27 % Condensation attempts : 0
% 26.02/4.27 % Condensation successes : 0
% 26.02/4.27 % Termbank termtop insertions : 6378625
% 26.02/4.27 % Search garbage collected termcells : 2
% 26.02/4.27
% 26.02/4.27 % -------------------------------------------------
% 26.02/4.27 % User time : 3.515 s
% 26.02/4.27 % System time : 0.173 s
% 26.02/4.27 % Total time : 3.688 s
% 26.02/4.27 % Maximum resident set size: 3644 pages
% 26.02/4.27
% 26.02/4.27 % -------------------------------------------------
% 26.02/4.27 % User time : 3.515 s
% 26.02/4.27 % System time : 0.179 s
% 26.02/4.27 % Total time : 3.694 s
% 26.02/4.27 % Maximum resident set size: 4608 pages
% 26.02/4.27 % E exiting
%------------------------------------------------------------------------------