%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP170-4 : 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 : n004.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 12:38:50 PM UTC 2026
% Result : Unsatisfiable 5.46s 1.25s
% Output : CNFRefutation 5.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 15 RR)
% Number of literals : 60 ( 59 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 : 93 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
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(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(p03d_1,hypothesis,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GRP004-2.ax',lub_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/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
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(p03d_2,hypothesis,
greatest_lower_bound(c,d) = c,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',prove_p03d) ).
cnf(c_0_15,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_16,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_17,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_18,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_19,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_20,plain,
multiply(inverse(inverse(inverse(X1))),X1) = identity,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_22,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_23,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_20]),c_0_19]) ).
cnf(c_0_24,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,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_26,hypothesis,
least_upper_bound(a,b) = b,
p03d_1 ).
cnf(c_0_27,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_28,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_16,c_0_23]) ).
cnf(c_0_29,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_30,plain,
greatest_lower_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,hypothesis,
least_upper_bound(b,a) = b,
inference(rw,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_32,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_33,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_27,c_0_28]),c_0_29]) ).
cnf(c_0_34,hypothesis,
greatest_lower_bound(a,least_upper_bound(X1,b)) = a,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X1,X2),inverse(X2))) = identity,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,hypothesis,
greatest_lower_bound(a,least_upper_bound(b,X1)) = a,
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_37,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_29]) ).
cnf(c_0_38,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_39,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_40,hypothesis,
least_upper_bound(identity,multiply(a,inverse(least_upper_bound(b,X1)))) = identity,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,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_39,c_0_18]) ).
cnf(c_0_43,hypothesis,
least_upper_bound(identity,multiply(a,inverse(b))) = identity,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_45,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_46,hypothesis,
least_upper_bound(inverse(b),inverse(a)) = inverse(a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_44]),c_0_22]) ).
cnf(c_0_47,hypothesis,
greatest_lower_bound(c,d) = c,
p03d_2 ).
cnf(c_0_48,plain,
greatest_lower_bound(X1,multiply(X2,multiply(inverse(X3),X1))) = multiply(greatest_lower_bound(X3,X2),multiply(inverse(X3),X1)),
inference(spm,[status(thm)],[c_0_27,c_0_45]) ).
cnf(c_0_49,hypothesis,
greatest_lower_bound(inverse(b),inverse(a)) = inverse(b),
inference(spm,[status(thm)],[c_0_21,c_0_46]) ).
cnf(c_0_50,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_51,hypothesis,
greatest_lower_bound(c,greatest_lower_bound(d,X1)) = greatest_lower_bound(c,X1),
inference(spm,[status(thm)],[c_0_38,c_0_47]) ).
cnf(c_0_52,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_48,c_0_49]),c_0_23]),c_0_23]),c_0_18]) ).
cnf(c_0_53,negated_conjecture,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
inference(fof_simplification,[status(thm)],[prove_p03d]) ).
cnf(c_0_54,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_50,c_0_18]) ).
cnf(c_0_55,hypothesis,
greatest_lower_bound(c,multiply(inverse(a),multiply(b,d))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_47]) ).
cnf(c_0_56,negated_conjecture,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
c_0_53 ).
cnf(c_0_57,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_54,c_0_55]),c_0_23]),c_0_23]),c_0_29]) ).
cnf(c_0_58,negated_conjecture,
least_upper_bound(multiply(b,d),multiply(a,c)) != multiply(b,d),
inference(rw,[status(thm)],[c_0_56,c_0_22]) ).
cnf(c_0_59,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_57]),c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP170-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n004.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 20 20:03:19 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 5.46/1.25 % Version: 3.5.1
% 5.46/1.25 % Preprocessing class: FSMSSMSSSSSNFFN.
% 5.46/1.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.46/1.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.46/1.25 % Starting new_bool_3 with 300s (1) cores
% 5.46/1.25 % Starting new_bool_1 with 300s (1) cores
% 5.46/1.25 % Starting sh5l with 300s (1) cores
% 5.46/1.25 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1366330 completed with status 0
% 5.46/1.25 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 5.46/1.25 % Preprocessing class: FSMSSMSSSSSNFFN.
% 5.46/1.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.46/1.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.46/1.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.46/1.25 % No SInE strategy applied
% 5.46/1.25 % Search class: FUUPM-FFSF21-SFFFFFNN
% 5.46/1.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.46/1.25 % Starting SubtermCWHack with 136s (1) cores
% 5.46/1.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 5.46/1.25 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 5.46/1.25 % Starting new_bool_3 with 136s (1) cores
% 5.46/1.25 % Starting new_bool_1 with 136s (1) cores
% 5.46/1.25 % SubtermCWHack with pid 1366334 completed with status 0
% 5.46/1.25 % Result found by SubtermCWHack
% 5.46/1.25 % Preprocessing class: FSMSSMSSSSSNFFN.
% 5.46/1.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.46/1.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.46/1.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.46/1.25 % No SInE strategy applied
% 5.46/1.25 % Search class: FUUPM-FFSF21-SFFFFFNN
% 5.46/1.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.46/1.25 % Starting SubtermCWHack with 136s (1) cores
% 5.46/1.25 % Preprocessing time : 0.001 s
% 5.46/1.25
% 5.46/1.25 % Proof found!
% 5.46/1.25 % SZS status Unsatisfiable
% 5.46/1.25 % SZS output start CNFRefutation
% See solution above
% 5.46/1.25 % Parsed axioms : 18
% 5.46/1.25 % Removed by relevancy pruning/SinE : 0
% 5.46/1.25 % Initial clauses : 18
% 5.46/1.25 % Removed in clause preprocessing : 0
% 5.46/1.25 % Initial clauses in saturation : 18
% 5.46/1.25 % Processed clauses : 3402
% 5.46/1.25 % ...of these trivial : 1450
% 5.46/1.25 % ...subsumed : 1369
% 5.46/1.25 % ...remaining for further processing : 583
% 5.46/1.25 % Other redundant clauses eliminated : 0
% 5.46/1.25 % Clauses deleted for lack of memory : 0
% 5.46/1.25 % Backward-subsumed : 0
% 5.46/1.25 % Backward-rewritten : 43
% 5.46/1.25 % Generated clauses : 83751
% 5.46/1.25 % ...of the previous two non-redundant : 48357
% 5.46/1.25 % ...aggressively subsumed : 0
% 5.46/1.25 % Contextual simplify-reflections : 0
% 5.46/1.25 % Paramodulations : 83751
% 5.46/1.25 % Factorizations : 0
% 5.46/1.25 % NegExts : 0
% 5.46/1.25 % Equation resolutions : 0
% 5.46/1.25 % Disequality decompositions : 0
% 5.46/1.25 % Total rewrite steps : 102287
% 5.46/1.25 % ...of those cached : 78410
% 5.46/1.25 % Propositional unsat checks : 0
% 5.46/1.25 % Propositional check models : 0
% 5.46/1.25 % Propositional check unsatisfiable : 0
% 5.46/1.25 % Propositional clauses : 0
% 5.46/1.25 % Propositional clauses after purity: 0
% 5.46/1.25 % Propositional unsat core size : 0
% 5.46/1.25 % Propositional preprocessing time : 0.000
% 5.46/1.25 % Propositional encoding time : 0.000
% 5.46/1.25 % Propositional solver time : 0.000
% 5.46/1.25 % Success case prop preproc time : 0.000
% 5.46/1.25 % Success case prop encoding time : 0.000
% 5.46/1.25 % Success case prop solver time : 0.000
% 5.46/1.25 % Current number of processed clauses : 540
% 5.46/1.25 % Positive orientable unit clauses : 507
% 5.46/1.25 % Positive unorientable unit clauses: 32
% 5.46/1.25 % Negative unit clauses : 1
% 5.46/1.25 % Non-unit-clauses : 0
% 5.46/1.25 % Current number of unprocessed clauses: 44724
% 5.46/1.25 % ...number of literals in the above : 44724
% 5.46/1.25 % Current number of archived formulas : 0
% 5.46/1.25 % Current number of archived clauses : 43
% 5.46/1.25 % Clause-clause subsumption calls (NU) : 0
% 5.46/1.25 % Rec. Clause-clause subsumption calls : 0
% 5.46/1.25 % Non-unit clause-clause subsumptions : 0
% 5.46/1.25 % Unit Clause-clause subsumption calls : 83
% 5.46/1.25 % Rewrite failures with RHS unbound : 0
% 5.46/1.25 % BW rewrite match attempts : 2036
% 5.46/1.25 % BW rewrite match successes : 465
% 5.46/1.25 % Condensation attempts : 0
% 5.46/1.25 % Condensation successes : 0
% 5.46/1.25 % Termbank termtop insertions : 898464
% 5.46/1.25 % Search garbage collected termcells : 2
% 5.46/1.25
% 5.46/1.25 % -------------------------------------------------
% 5.46/1.25 % User time : 0.641 s
% 5.46/1.25 % System time : 0.040 s
% 5.46/1.25 % Total time : 0.681 s
% 5.46/1.25 % Maximum resident set size: 3640 pages
% 5.46/1.25
% 5.46/1.25 % -------------------------------------------------
% 5.46/1.25 % User time : 3.126 s
% 5.46/1.25 % System time : 0.188 s
% 5.46/1.25 % Total time : 3.315 s
% 5.46/1.25 % Maximum resident set size: 4864 pages
% 5.46/1.25 % E exiting
%------------------------------------------------------------------------------