%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP170-4 : 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 : n015.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 12:42:44 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.82s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of clauses : 66 ( 66 unt; 0 nHn; 14 RR)
% Number of literals : 66 ( 65 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 111 ( 10 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(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(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(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/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
cnf(idempotence_of_lub,axiom,
least_upper_bound(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_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/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
cnf(p03d_1,hypothesis,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p03d_1) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
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/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
cnf(p03d_2,hypothesis,
greatest_lower_bound(c,d) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p03d_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(prove_p03d,negated_conjecture,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p03d) ).
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(c_0_17,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_18,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_19,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_20,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_21,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_22,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_20]) ).
cnf(c_0_23,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_23]) ).
cnf(c_0_25,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_26,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_27,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_28,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_29,axiom,
least_upper_bound(X1,X1) = X1,
idempotence_of_lub ).
cnf(c_0_30,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_31,plain,
least_upper_bound(identity,multiply(inverse(X1),X2)) = multiply(inverse(X1),least_upper_bound(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_18]),c_0_27]) ).
cnf(c_0_32,plain,
least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
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,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_24]) ).
cnf(c_0_35,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_30]),c_0_23]) ).
cnf(c_0_36,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_18]) ).
cnf(c_0_37,plain,
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_25]) ).
cnf(c_0_38,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_40,plain,
multiply(inverse(X1),least_upper_bound(X2,multiply(X1,X3))) = least_upper_bound(multiply(inverse(X1),X2),X3),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_41,plain,
least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X1,X2)))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_23]) ).
cnf(c_0_42,plain,
least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X1,X2),X3))) = least_upper_bound(X1,X2),
inference(spm,[status(thm)],[c_0_39,c_0_28]) ).
cnf(c_0_43,plain,
least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_23]),c_0_23]) ).
cnf(c_0_44,plain,
least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(least_upper_bound(X2,X1),X3))) = least_upper_bound(X2,X1),
inference(spm,[status(thm)],[c_0_42,c_0_27]) ).
cnf(c_0_45,hypothesis,
least_upper_bound(a,b) = b,
p03d_1 ).
cnf(c_0_46,plain,
least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(X1),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,hypothesis,
least_upper_bound(b,a) = b,
inference(rw,[status(thm)],[c_0_45,c_0_27]) ).
cnf(c_0_48,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_49,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_50,hypothesis,
least_upper_bound(inverse(b),inverse(a)) = inverse(a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_27]) ).
cnf(c_0_51,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_52,hypothesis,
greatest_lower_bound(c,d) = c,
p03d_2 ).
cnf(c_0_53,plain,
greatest_lower_bound(X1,multiply(X2,multiply(X3,X1))) = multiply(greatest_lower_bound(inverse(X3),X2),multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_48,c_0_20]) ).
cnf(c_0_54,hypothesis,
greatest_lower_bound(inverse(b),inverse(a)) = inverse(b),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_56,hypothesis,
greatest_lower_bound(c,greatest_lower_bound(d,X1)) = greatest_lower_bound(c,X1),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,hypothesis,
greatest_lower_bound(X1,multiply(inverse(a),multiply(b,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_20]) ).
cnf(c_0_58,negated_conjecture,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
inference(fof_simplification,[status(thm)],[prove_p03d]) ).
cnf(c_0_59,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_55,c_0_20]) ).
cnf(c_0_60,hypothesis,
greatest_lower_bound(c,multiply(inverse(a),multiply(b,d))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_52]) ).
cnf(c_0_61,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_62,negated_conjecture,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
c_0_58 ).
cnf(c_0_63,hypothesis,
greatest_lower_bound(multiply(b,d),multiply(a,c)) = multiply(a,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_24]),c_0_24]),c_0_61]) ).
cnf(c_0_64,negated_conjecture,
least_upper_bound(multiply(b,d),multiply(a,c)) != multiply(b,d),
inference(rw,[status(thm)],[c_0_62,c_0_27]) ).
cnf(c_0_65,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_63]),c_0_64]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP170-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.37 % Computer : n015.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sun Sep 20 20:06:56 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.82 % Version: 3.5.1
% 0.15/5.82 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.82 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.82 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.82 % Starting sh5l with 300s (1) cores
% 0.15/5.82 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3810644 completed with status 0
% 0.15/5.82 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/5.82 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.82 % No SInE strategy applied
% 0.15/5.82 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.15/5.82 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.82 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/5.82 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.15/5.82 % Starting new_bool_3 with 136s (1) cores
% 0.15/5.82 % Starting new_bool_1 with 136s (1) cores
% 0.15/5.82 % SAT001_MinMin_p005000_rr_RG with pid 3810651 completed with status 0
% 0.15/5.82 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.15/5.82 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.82 % No SInE strategy applied
% 0.15/5.82 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.15/5.82 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.82 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/5.82 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.15/5.82 % Preprocessing time : 0.001 s
% 0.15/5.82 % Presaturation interreduction done
% 0.15/5.82
% 0.15/5.82 % Proof found!
% 0.15/5.82 % SZS status Unsatisfiable
% 0.15/5.82 % SZS output start CNFRefutation
% See solution above
% 0.15/5.82 % Parsed axioms : 18
% 0.15/5.82 % Removed by relevancy pruning/SinE : 0
% 0.15/5.82 % Initial clauses : 18
% 0.15/5.82 % Removed in clause preprocessing : 0
% 0.15/5.82 % Initial clauses in saturation : 18
% 0.15/5.82 % Processed clauses : 3073
% 0.15/5.82 % ...of these trivial : 1705
% 0.15/5.82 % ...subsumed : 772
% 0.15/5.82 % ...remaining for further processing : 596
% 0.15/5.82 % Other redundant clauses eliminated : 0
% 0.15/5.82 % Clauses deleted for lack of memory : 0
% 0.15/5.82 % Backward-subsumed : 0
% 0.15/5.82 % Backward-rewritten : 56
% 0.15/5.82 % Generated clauses : 63669
% 0.15/5.82 % ...of the previous two non-redundant : 36169
% 0.15/5.82 % ...aggressively subsumed : 0
% 0.15/5.82 % Contextual simplify-reflections : 0
% 0.15/5.82 % Paramodulations : 63669
% 0.15/5.82 % Factorizations : 0
% 0.15/5.82 % NegExts : 0
% 0.15/5.82 % Equation resolutions : 0
% 0.15/5.82 % Disequality decompositions : 0
% 0.15/5.82 % Total rewrite steps : 80041
% 0.15/5.82 % ...of those cached : 60990
% 0.15/5.82 % Propositional unsat checks : 0
% 0.15/5.82 % Propositional check models : 0
% 0.15/5.82 % Propositional check unsatisfiable : 0
% 0.15/5.82 % Propositional clauses : 0
% 0.15/5.82 % Propositional clauses after purity: 0
% 0.15/5.82 % Propositional unsat core size : 0
% 0.15/5.82 % Propositional preprocessing time : 0.000
% 0.15/5.82 % Propositional encoding time : 0.000
% 0.15/5.82 % Propositional solver time : 0.000
% 0.15/5.82 % Success case prop preproc time : 0.000
% 0.15/5.82 % Success case prop encoding time : 0.000
% 0.15/5.82 % Success case prop solver time : 0.000
% 0.15/5.82 % Current number of processed clauses : 522
% 0.15/5.82 % Positive orientable unit clauses : 498
% 0.15/5.82 % Positive unorientable unit clauses: 23
% 0.15/5.82 % Negative unit clauses : 1
% 0.15/5.82 % Non-unit-clauses : 0
% 0.15/5.82 % Current number of unprocessed clauses: 33002
% 0.15/5.82 % ...number of literals in the above : 33002
% 0.15/5.82 % Current number of archived formulas : 0
% 0.15/5.82 % Current number of archived clauses : 74
% 0.15/5.82 % Clause-clause subsumption calls (NU) : 0
% 0.15/5.82 % Rec. Clause-clause subsumption calls : 0
% 0.15/5.82 % Non-unit clause-clause subsumptions : 0
% 0.15/5.82 % Unit Clause-clause subsumption calls : 101
% 0.15/5.82 % Rewrite failures with RHS unbound : 0
% 0.15/5.82 % BW rewrite match attempts : 2156
% 0.15/5.82 % BW rewrite match successes : 436
% 0.15/5.82 % Condensation attempts : 0
% 0.15/5.82 % Condensation successes : 0
% 0.15/5.82 % Termbank termtop insertions : 796631
% 0.15/5.82 % Search garbage collected termcells : 2
% 0.15/5.82
% 0.15/5.82 % -------------------------------------------------
% 0.15/5.82 % User time : 0.339 s
% 0.15/5.82 % System time : 0.025 s
% 0.15/5.82 % Total time : 0.364 s
% 0.15/5.82 % Maximum resident set size: 3640 pages
% 0.15/5.82
% 0.15/5.82 % -------------------------------------------------
% 0.15/5.82 % User time : 1.720 s
% 0.15/5.82 % System time : 0.121 s
% 0.15/5.82 % Total time : 1.841 s
% 0.15/5.82 % Maximum resident set size: 4864 pages
% 0.15/5.82 % E exiting
%------------------------------------------------------------------------------