%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP170-3 : 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 : n003.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 1.59s 0.66s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 51 ( 51 unt; 0 nHn; 14 RR)
% Number of literals : 51 ( 50 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; 5 con; 0-2 aty)
% Number of variables : 76 ( 6 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_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(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(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(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(p03c_1,hypothesis,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p03c_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(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(p03c_2,hypothesis,
least_upper_bound(c,d) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p03c_2) ).
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(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_p03c,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p03c) ).
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,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_19,plain,
multiply(inverse(inverse(inverse(X1))),X1) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_18]) ).
cnf(c_0_21,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_22,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_23,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_24,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_25,plain,
greatest_lower_bound(identity,multiply(X1,inverse(X2))) = multiply(greatest_lower_bound(X1,X2),inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_26,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_27,hypothesis,
least_upper_bound(a,b) = b,
p03c_1 ).
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,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X1,X2),inverse(X2))) = identity,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,hypothesis,
greatest_lower_bound(a,b) = a,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_32,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_28,c_0_17]) ).
cnf(c_0_33,hypothesis,
least_upper_bound(identity,multiply(a,inverse(b))) = identity,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_35,hypothesis,
least_upper_bound(c,d) = d,
p03c_2 ).
cnf(c_0_36,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_37,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_38,hypothesis,
least_upper_bound(inverse(a),inverse(b)) = inverse(a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_34]) ).
cnf(c_0_39,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_40,hypothesis,
greatest_lower_bound(c,d) = c,
inference(spm,[status(thm)],[c_0_26,c_0_35]) ).
cnf(c_0_41,plain,
greatest_lower_bound(X1,multiply(X2,multiply(inverse(X3),X1))) = multiply(greatest_lower_bound(X2,X3),multiply(inverse(X3),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_36]),c_0_23]) ).
cnf(c_0_42,hypothesis,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_23]) ).
cnf(c_0_43,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_44,hypothesis,
greatest_lower_bound(c,greatest_lower_bound(d,X1)) = greatest_lower_bound(c,X1),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,hypothesis,
greatest_lower_bound(X1,multiply(inverse(a),multiply(b,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_20]),c_0_20]),c_0_17]) ).
cnf(c_0_46,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
inference(fof_simplification,[status(thm)],[prove_p03c]) ).
cnf(c_0_47,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_43,c_0_17]) ).
cnf(c_0_48,hypothesis,
greatest_lower_bound(c,multiply(inverse(a),multiply(b,d))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_40]) ).
cnf(c_0_49,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
c_0_46 ).
cnf(c_0_50,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_20]),c_0_20]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP170-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 20:05:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 1.59/0.66 % Version: 3.5.1
% 1.59/0.66 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.59/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.59/0.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.59/0.66 % Starting new_bool_3 with 300s (1) cores
% 1.59/0.66 % Starting new_bool_1 with 300s (1) cores
% 1.59/0.66 % Starting sh5l with 300s (1) cores
% 1.59/0.66 % sh5l with pid 2461153 completed with status 0
% 1.59/0.66 % Result found by sh5l
% 1.59/0.66 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.59/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.59/0.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.59/0.66 % Starting new_bool_3 with 300s (1) cores
% 1.59/0.66 % Starting new_bool_1 with 300s (1) cores
% 1.59/0.66 % Starting sh5l with 300s (1) cores
% 1.59/0.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 1.59/0.66 % SinE strategy is gf500_gu_R04_F100_L20000
% 1.59/0.66 % Search class: FUUPM-FFSF21-SFFFFFNN
% 1.59/0.66 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.59/0.66 % Starting SubtermCWHack with 31s (1) cores
% 1.59/0.66 % SubtermCWHack with pid 2461160 completed with status 0
% 1.59/0.66 % Result found by SubtermCWHack
% 1.59/0.66 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.59/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.59/0.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.59/0.66 % Starting new_bool_3 with 300s (1) cores
% 1.59/0.66 % Starting new_bool_1 with 300s (1) cores
% 1.59/0.66 % Starting sh5l with 300s (1) cores
% 1.59/0.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 1.59/0.66 % SinE strategy is gf500_gu_R04_F100_L20000
% 1.59/0.66 % Search class: FUUPM-FFSF21-SFFFFFNN
% 1.59/0.66 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.59/0.66 % Starting SubtermCWHack with 31s (1) cores
% 1.59/0.66 % Preprocessing time : 0.001 s
% 1.59/0.66
% 1.59/0.66 % Proof found!
% 1.59/0.66 % SZS status Unsatisfiable
% 1.59/0.66 % SZS output start CNFRefutation
% See solution above
% 1.59/0.66 % Parsed axioms : 18
% 1.59/0.66 % Removed by relevancy pruning/SinE : 0
% 1.59/0.66 % Initial clauses : 18
% 1.59/0.66 % Removed in clause preprocessing : 0
% 1.59/0.66 % Initial clauses in saturation : 18
% 1.59/0.66 % Processed clauses : 1148
% 1.59/0.66 % ...of these trivial : 420
% 1.59/0.66 % ...subsumed : 403
% 1.59/0.66 % ...remaining for further processing : 325
% 1.59/0.66 % Other redundant clauses eliminated : 0
% 1.59/0.66 % Clauses deleted for lack of memory : 0
% 1.59/0.66 % Backward-subsumed : 0
% 1.59/0.66 % Backward-rewritten : 33
% 1.59/0.66 % Generated clauses : 27008
% 1.59/0.66 % ...of the previous two non-redundant : 15101
% 1.59/0.66 % ...aggressively subsumed : 0
% 1.59/0.66 % Contextual simplify-reflections : 0
% 1.59/0.66 % Paramodulations : 27008
% 1.59/0.66 % Factorizations : 0
% 1.59/0.66 % NegExts : 0
% 1.59/0.66 % Equation resolutions : 0
% 1.59/0.66 % Disequality decompositions : 0
% 1.59/0.66 % Total rewrite steps : 31233
% 1.59/0.66 % ...of those cached : 23276
% 1.59/0.66 % Propositional unsat checks : 0
% 1.59/0.66 % Propositional check models : 0
% 1.59/0.66 % Propositional check unsatisfiable : 0
% 1.59/0.66 % Propositional clauses : 0
% 1.59/0.66 % Propositional clauses after purity: 0
% 1.59/0.66 % Propositional unsat core size : 0
% 1.59/0.66 % Propositional preprocessing time : 0.000
% 1.59/0.66 % Propositional encoding time : 0.000
% 1.59/0.66 % Propositional solver time : 0.000
% 1.59/0.66 % Success case prop preproc time : 0.000
% 1.59/0.66 % Success case prop encoding time : 0.000
% 1.59/0.66 % Success case prop solver time : 0.000
% 1.59/0.66 % Current number of processed clauses : 292
% 1.59/0.66 % Positive orientable unit clauses : 268
% 1.59/0.66 % Positive unorientable unit clauses: 23
% 1.59/0.66 % Negative unit clauses : 1
% 1.59/0.66 % Non-unit-clauses : 0
% 1.59/0.66 % Current number of unprocessed clauses: 13915
% 1.59/0.66 % ...number of literals in the above : 13915
% 1.59/0.66 % Current number of archived formulas : 0
% 1.59/0.66 % Current number of archived clauses : 33
% 1.59/0.66 % Clause-clause subsumption calls (NU) : 0
% 1.59/0.66 % Rec. Clause-clause subsumption calls : 0
% 1.59/0.66 % Non-unit clause-clause subsumptions : 0
% 1.59/0.66 % Unit Clause-clause subsumption calls : 48
% 1.59/0.66 % Rewrite failures with RHS unbound : 0
% 1.59/0.66 % BW rewrite match attempts : 727
% 1.59/0.66 % BW rewrite match successes : 331
% 1.59/0.66 % Condensation attempts : 0
% 1.59/0.66 % Condensation successes : 0
% 1.59/0.66 % Termbank termtop insertions : 258452
% 1.59/0.66 % Search garbage collected termcells : 2
% 1.59/0.66
% 1.59/0.66 % -------------------------------------------------
% 1.59/0.66 % User time : 0.203 s
% 1.59/0.66 % System time : 0.017 s
% 1.59/0.66 % Total time : 0.220 s
% 1.59/0.66 % Maximum resident set size: 3588 pages
% 1.59/0.66
% 1.59/0.66 % -------------------------------------------------
% 1.59/0.66 % User time : 0.206 s
% 1.59/0.66 % System time : 0.019 s
% 1.59/0.66 % Total time : 0.226 s
% 1.59/0.66 % Maximum resident set size: 4864 pages
% 1.59/0.66 % E exiting
%------------------------------------------------------------------------------