%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP184-2 : 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 : n011.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 12:38:54 PM UTC 2026
% Result : Unsatisfiable 1.22s 0.78s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 8 RR)
% Number of literals : 37 ( 36 equ; 5 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(p21_3,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_3) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(p21_1,hypothesis,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_1) ).
cnf(p21_2,hypothesis,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_2) ).
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(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
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_p21,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p21) ).
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(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(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(c_0_12,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
p21_3 ).
cnf(c_0_13,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_14,hypothesis,
inverse(identity) = identity,
p21_1 ).
cnf(c_0_15,hypothesis,
multiply(inverse(X1),identity) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_16,hypothesis,
inverse(inverse(X1)) = X1,
p21_2 ).
cnf(c_0_17,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_18,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_19,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
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,hypothesis,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_13]),c_0_18]) ).
cnf(c_0_23,hypothesis,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_24,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(fof_simplification,[status(thm)],[prove_p21]) ).
cnf(c_0_25,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_20,c_0_21]),c_0_18]) ).
cnf(c_0_26,hypothesis,
greatest_lower_bound(identity,inverse(X1)) = multiply(greatest_lower_bound(X1,identity),inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18]) ).
cnf(c_0_27,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
c_0_24 ).
cnf(c_0_28,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_29,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_30,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_31,hypothesis,
multiply(inverse(X1),greatest_lower_bound(X1,identity)) = multiply(greatest_lower_bound(X1,identity),inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_18]),c_0_26]) ).
cnf(c_0_32,negated_conjecture,
least_upper_bound(multiply(inverse(greatest_lower_bound(identity,a)),identity),multiply(inverse(greatest_lower_bound(identity,a)),a)) != least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_18]),c_0_28]),c_0_28]),c_0_18]),c_0_29]),c_0_30]),c_0_13]) ).
cnf(c_0_33,hypothesis,
multiply(inverse(greatest_lower_bound(X1,identity)),X1) = multiply(X1,inverse(greatest_lower_bound(X1,identity))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_31]),c_0_12]),c_0_16]),c_0_16]) ).
cnf(c_0_34,negated_conjecture,
least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(inverse(greatest_lower_bound(identity,a)),a)) != least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a)))),
inference(rw,[status(thm)],[c_0_32,c_0_15]) ).
cnf(c_0_35,hypothesis,
multiply(inverse(greatest_lower_bound(identity,X1)),X1) = multiply(X1,inverse(greatest_lower_bound(identity,X1))),
inference(spm,[status(thm)],[c_0_33,c_0_18]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP184-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.45 % Computer : n011.cluster.edu
% 0.21/0.45 % Model : x86_64 x86_64
% 0.21/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.45 % Memory : 8046.5625MB
% 0.21/0.45 % OS : Linux 6.8.0-71-generic
% 0.21/0.45 % CPULimit : 300
% 0.21/0.45 % WCLimit : 300
% 0.21/0.45 % DateTime : Sun Sep 20 20:05:10 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.53 Running first-order theorem proving
% 0.24/0.53 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
% 1.22/0.78 % Version: 3.5.1
% 1.22/0.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.22/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.22/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.22/0.78 % Starting new_bool_3 with 300s (1) cores
% 1.22/0.78 % Starting new_bool_1 with 300s (1) cores
% 1.22/0.78 % Starting sh5l with 300s (1) cores
% 1.22/0.78 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 53781 completed with status 0
% 1.22/0.78 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.22/0.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.22/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.22/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.22/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.22/0.78 % No SInE strategy applied
% 1.22/0.78 % Search class: FUUPM-FFSF21-MFFFFFNN
% 1.22/0.78 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 1.22/0.78 % Starting SubtermCWHack with 136s (1) cores
% 1.22/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.22/0.78 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 1.22/0.78 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 1.22/0.78 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 1.22/0.78 % U----_043_B31_F1_PI_AE_CS_SP_S2S with pid 53791 completed with status 0
% 1.22/0.78 % Result found by U----_043_B31_F1_PI_AE_CS_SP_S2S
% 1.22/0.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.22/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.22/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.22/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.22/0.78 % No SInE strategy applied
% 1.22/0.78 % Search class: FUUPM-FFSF21-MFFFFFNN
% 1.22/0.78 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 1.22/0.78 % Starting SubtermCWHack with 136s (1) cores
% 1.22/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.22/0.78 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 1.22/0.78 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 1.22/0.78 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 1.22/0.78 % Preprocessing time : 0.002 s
% 1.22/0.78
% 1.22/0.78 % Proof found!
% 1.22/0.78 % SZS status Unsatisfiable
% 1.22/0.78 % SZS output start CNFRefutation
% See solution above
% 1.22/0.78 % Parsed axioms : 19
% 1.22/0.78 % Removed by relevancy pruning/SinE : 0
% 1.22/0.78 % Initial clauses : 19
% 1.22/0.78 % Removed in clause preprocessing : 0
% 1.22/0.78 % Initial clauses in saturation : 19
% 1.22/0.78 % Processed clauses : 459
% 1.22/0.78 % ...of these trivial : 174
% 1.22/0.78 % ...subsumed : 161
% 1.22/0.78 % ...remaining for further processing : 124
% 1.22/0.78 % Other redundant clauses eliminated : 0
% 1.22/0.78 % Clauses deleted for lack of memory : 0
% 1.22/0.78 % Backward-subsumed : 0
% 1.22/0.78 % Backward-rewritten : 10
% 1.22/0.78 % Generated clauses : 6262
% 1.22/0.78 % ...of the previous two non-redundant : 3800
% 1.22/0.78 % ...aggressively subsumed : 0
% 1.22/0.78 % Contextual simplify-reflections : 0
% 1.22/0.78 % Paramodulations : 6262
% 1.22/0.78 % Factorizations : 0
% 1.22/0.78 % NegExts : 0
% 1.22/0.78 % Equation resolutions : 0
% 1.22/0.78 % Disequality decompositions : 0
% 1.22/0.78 % Total rewrite steps : 8222
% 1.22/0.78 % ...of those cached : 5959
% 1.22/0.78 % Propositional unsat checks : 0
% 1.22/0.78 % Propositional check models : 0
% 1.22/0.78 % Propositional check unsatisfiable : 0
% 1.22/0.78 % Propositional clauses : 0
% 1.22/0.78 % Propositional clauses after purity: 0
% 1.22/0.78 % Propositional unsat core size : 0
% 1.22/0.78 % Propositional preprocessing time : 0.000
% 1.22/0.78 % Propositional encoding time : 0.000
% 1.22/0.78 % Propositional solver time : 0.000
% 1.22/0.78 % Success case prop preproc time : 0.000
% 1.22/0.78 % Success case prop encoding time : 0.000
% 1.22/0.78 % Success case prop solver time : 0.000
% 1.22/0.78 % Current number of processed clauses : 114
% 1.22/0.78 % Positive orientable unit clauses : 102
% 1.22/0.78 % Positive unorientable unit clauses: 12
% 1.22/0.78 % Negative unit clauses : 0
% 1.22/0.78 % Non-unit-clauses : 0
% 1.22/0.78 % Current number of unprocessed clauses: 3333
% 1.22/0.78 % ...number of literals in the above : 3333
% 1.22/0.78 % Current number of archived formulas : 0
% 1.22/0.78 % Current number of archived clauses : 10
% 1.22/0.78 % Clause-clause subsumption calls (NU) : 0
% 1.22/0.78 % Rec. Clause-clause subsumption calls : 0
% 1.22/0.78 % Non-unit clause-clause subsumptions : 0
% 1.22/0.78 % Unit Clause-clause subsumption calls : 32
% 1.22/0.78 % Rewrite failures with RHS unbound : 0
% 1.22/0.78 % BW rewrite match attempts : 275
% 1.22/0.78 % BW rewrite match successes : 159
% 1.22/0.78 % Condensation attempts : 0
% 1.22/0.78 % Condensation successes : 0
% 1.22/0.78 % Termbank termtop insertions : 57580
% 1.22/0.78 % Search garbage collected termcells : 2
% 1.22/0.78
% 1.22/0.78 % -------------------------------------------------
% 1.22/0.78 % User time : 0.086 s
% 1.22/0.78 % System time : 0.016 s
% 1.22/0.78 % Total time : 0.101 s
% 1.22/0.78 % Maximum resident set size: 3640 pages
% 1.22/0.78
% 1.22/0.78 % -------------------------------------------------
% 1.22/0.78 % User time : 0.626 s
% 1.22/0.78 % System time : 0.082 s
% 1.22/0.78 % Total time : 0.708 s
% 1.22/0.78 % Maximum resident set size: 4864 pages
% 1.22/0.78 % E exiting
%------------------------------------------------------------------------------