%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP181-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:38:53 PM UTC 2026
% Result : Unsatisfiable 60.36s 9.37s
% Output : CNFRefutation 60.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 12 RR)
% Number of literals : 40 ( 39 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 : 55 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(p12x_3,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_3) ).
cnf(p12x_2,hypothesis,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_2) ).
cnf(monotony_glb1,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
cnf(p12x_6,hypothesis,
inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(X1),inverse(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_6) ).
cnf(p12x_1,hypothesis,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_1) ).
cnf(monotony_lub1,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
cnf(p12x_5,hypothesis,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_5) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
cnf(p12x_4,hypothesis,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_4) ).
cnf(prove_p12x,negated_conjecture,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p12x) ).
cnf(c_0_14,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_15,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_16,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_17,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_18,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
p12x_3 ).
cnf(c_0_19,hypothesis,
inverse(inverse(X1)) = X1,
p12x_2 ).
cnf(c_0_20,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_21,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_22,hypothesis,
inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(X1),inverse(X2)),
p12x_6 ).
cnf(c_0_23,hypothesis,
inverse(identity) = identity,
p12x_1 ).
cnf(c_0_24,hypothesis,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_25,plain,
greatest_lower_bound(identity,multiply(inverse(X1),X2)) = multiply(inverse(X1),greatest_lower_bound(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_15]),c_0_21]) ).
cnf(c_0_26,hypothesis,
inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,hypothesis,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_28,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_29,hypothesis,
multiply(greatest_lower_bound(X1,X2),least_upper_bound(identity,multiply(inverse(X1),X2))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_19]) ).
cnf(c_0_30,plain,
least_upper_bound(identity,multiply(inverse(X1),X2)) = multiply(inverse(X1),least_upper_bound(X1,X2)),
inference(spm,[status(thm)],[c_0_28,c_0_15]) ).
cnf(c_0_31,hypothesis,
least_upper_bound(a,c) = least_upper_bound(b,c),
p12x_5 ).
cnf(c_0_32,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_33,hypothesis,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
p12x_4 ).
cnf(c_0_34,negated_conjecture,
a != b,
inference(fof_simplification,[status(thm)],[prove_p12x]) ).
cnf(c_0_35,hypothesis,
multiply(greatest_lower_bound(X1,X2),multiply(inverse(X1),least_upper_bound(X1,X2))) = X2,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,hypothesis,
least_upper_bound(c,a) = least_upper_bound(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]) ).
cnf(c_0_37,hypothesis,
greatest_lower_bound(c,a) = greatest_lower_bound(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_21]),c_0_21]) ).
cnf(c_0_38,negated_conjecture,
a != b,
c_0_34 ).
cnf(c_0_39,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_35]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP181-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n014.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 20 20:04:20 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.46 Running first-order theorem proving
% 0.16/0.46 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
% 60.36/9.37 % Version: 3.5.1
% 60.36/9.37 % Preprocessing class: FSMSSMSSSSSNFFN.
% 60.36/9.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 60.36/9.37 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 60.36/9.37 % Starting new_bool_3 with 300s (1) cores
% 60.36/9.37 % Starting new_bool_1 with 300s (1) cores
% 60.36/9.37 % Starting sh5l with 300s (1) cores
% 60.36/9.37 % new_bool_3 with pid 2231278 completed with status 0
% 60.36/9.37 % Result found by new_bool_3
% 60.36/9.37 % Preprocessing class: FSMSSMSSSSSNFFN.
% 60.36/9.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 60.36/9.37 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 60.36/9.37 % Starting new_bool_3 with 300s (1) cores
% 60.36/9.37 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 60.36/9.37 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 60.36/9.37 % Search class: FUUPM-FFSS21-SFFFFFNN
% 60.36/9.37 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 60.36/9.37 % Starting SubtermCWHack with 31s (1) cores
% 60.36/9.37 % SubtermCWHack with pid 2231284 completed with status 0
% 60.36/9.37 % Result found by SubtermCWHack
% 60.36/9.37 % Preprocessing class: FSMSSMSSSSSNFFN.
% 60.36/9.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 60.36/9.37 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 60.36/9.37 % Starting new_bool_3 with 300s (1) cores
% 60.36/9.37 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 60.36/9.37 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 60.36/9.37 % Search class: FUUPM-FFSS21-SFFFFFNN
% 60.36/9.37 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 60.36/9.37 % Starting SubtermCWHack with 31s (1) cores
% 60.36/9.37 % Preprocessing time : 0.001 s
% 60.36/9.37
% 60.36/9.37 % Proof found!
% 60.36/9.37 % SZS status Unsatisfiable
% 60.36/9.37 % SZS output start CNFRefutation
% See solution above
% 60.36/9.37 % Parsed axioms : 23
% 60.36/9.37 % Removed by relevancy pruning/SinE : 0
% 60.36/9.37 % Initial clauses : 23
% 60.36/9.37 % Removed in clause preprocessing : 0
% 60.36/9.37 % Initial clauses in saturation : 23
% 60.36/9.37 % Processed clauses : 19852
% 60.36/9.37 % ...of these trivial : 8010
% 60.36/9.37 % ...subsumed : 10376
% 60.36/9.37 % ...remaining for further processing : 1466
% 60.36/9.37 % Other redundant clauses eliminated : 0
% 60.36/9.37 % Clauses deleted for lack of memory : 0
% 60.36/9.37 % Backward-subsumed : 0
% 60.36/9.37 % Backward-rewritten : 109
% 60.36/9.37 % Generated clauses : 655880
% 60.36/9.37 % ...of the previous two non-redundant : 434626
% 60.36/9.37 % ...aggressively subsumed : 0
% 60.36/9.37 % Contextual simplify-reflections : 0
% 60.36/9.37 % Paramodulations : 655880
% 60.36/9.37 % Factorizations : 0
% 60.36/9.37 % NegExts : 0
% 60.36/9.37 % Equation resolutions : 0
% 60.36/9.37 % Disequality decompositions : 0
% 60.36/9.37 % Total rewrite steps : 1122462
% 60.36/9.37 % ...of those cached : 927803
% 60.36/9.37 % Propositional unsat checks : 0
% 60.36/9.37 % Propositional check models : 0
% 60.36/9.37 % Propositional check unsatisfiable : 0
% 60.36/9.37 % Propositional clauses : 0
% 60.36/9.37 % Propositional clauses after purity: 0
% 60.36/9.37 % Propositional unsat core size : 0
% 60.36/9.37 % Propositional preprocessing time : 0.000
% 60.36/9.37 % Propositional encoding time : 0.000
% 60.36/9.37 % Propositional solver time : 0.000
% 60.36/9.37 % Success case prop preproc time : 0.000
% 60.36/9.37 % Success case prop encoding time : 0.000
% 60.36/9.37 % Success case prop solver time : 0.000
% 60.36/9.37 % Current number of processed clauses : 1357
% 60.36/9.37 % Positive orientable unit clauses : 1306
% 60.36/9.37 % Positive unorientable unit clauses: 50
% 60.36/9.37 % Negative unit clauses : 1
% 60.36/9.37 % Non-unit-clauses : 0
% 60.36/9.37 % Current number of unprocessed clauses: 413744
% 60.36/9.37 % ...number of literals in the above : 413744
% 60.36/9.37 % Current number of archived formulas : 0
% 60.36/9.37 % Current number of archived clauses : 109
% 60.36/9.37 % Clause-clause subsumption calls (NU) : 0
% 60.36/9.37 % Rec. Clause-clause subsumption calls : 0
% 60.36/9.37 % Non-unit clause-clause subsumptions : 0
% 60.36/9.37 % Unit Clause-clause subsumption calls : 308
% 60.36/9.37 % Rewrite failures with RHS unbound : 0
% 60.36/9.37 % BW rewrite match attempts : 9274
% 60.36/9.37 % BW rewrite match successes : 671
% 60.36/9.37 % Condensation attempts : 0
% 60.36/9.37 % Condensation successes : 0
% 60.36/9.37 % Termbank termtop insertions : 9597899
% 60.36/9.37 % Search garbage collected termcells : 2
% 60.36/9.37
% 60.36/9.37 % -------------------------------------------------
% 60.36/9.37 % User time : 8.224 s
% 60.36/9.37 % System time : 0.337 s
% 60.36/9.37 % Total time : 8.561 s
% 60.36/9.37 % Maximum resident set size: 3640 pages
% 60.36/9.37
% 60.36/9.37 % -------------------------------------------------
% 60.36/9.37 % User time : 8.226 s
% 60.36/9.37 % System time : 0.345 s
% 60.36/9.37 % Total time : 8.571 s
% 60.36/9.37 % Maximum resident set size: 4864 pages
% 60.36/9.37 % E exiting
%------------------------------------------------------------------------------