%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP185-2 : 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 : n016.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 12:38:55 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.50s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 13
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 8 RR)
% Number of literals : 36 ( 35 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_p22a,negated_conjecture,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p22a) ).
cnf(p22a_3,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22a_3) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(p22a_1,hypothesis,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22a_1) ).
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(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(monotony_lub2,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
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(p22a_2,hypothesis,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22a_2) ).
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(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(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(idempotence_of_lub,axiom,
least_upper_bound(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_lub) ).
cnf(c_0_13,negated_conjecture,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(fof_simplification,[status(thm)],[prove_p22a]) ).
cnf(c_0_14,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
p22a_3 ).
cnf(c_0_15,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_16,hypothesis,
inverse(identity) = identity,
p22a_1 ).
cnf(c_0_17,negated_conjecture,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
c_0_13 ).
cnf(c_0_18,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_19,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_20,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_21,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_22,hypothesis,
multiply(inverse(X1),identity) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_23,hypothesis,
inverse(inverse(X1)) = X1,
p22a_2 ).
cnf(c_0_24,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_25,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_26,negated_conjecture,
least_upper_bound(identity,least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(multiply(a,identity),least_upper_bound(b,multiply(a,b)))))) != least_upper_bound(identity,least_upper_bound(multiply(a,identity),least_upper_bound(b,multiply(a,b)))),
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)],[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_19]),c_0_20]),c_0_15]),c_0_20]),c_0_15]),c_0_21]),c_0_21]),c_0_19]),c_0_20]),c_0_15]),c_0_20]),c_0_15]),c_0_21]) ).
cnf(c_0_27,hypothesis,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_30,axiom,
least_upper_bound(X1,X1) = X1,
idempotence_of_lub ).
cnf(c_0_31,negated_conjecture,
least_upper_bound(identity,least_upper_bound(multiply(a,b),least_upper_bound(identity,least_upper_bound(a,least_upper_bound(b,multiply(a,b)))))) != least_upper_bound(identity,least_upper_bound(a,least_upper_bound(b,multiply(a,b)))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X2,least_upper_bound(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_21]) ).
cnf(c_0_33,plain,
least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_21]) ).
cnf(c_0_34,plain,
least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]),c_0_33]),c_0_18]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP185-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 % Computer : n016.cluster.edu
% 0.10/0.41 % Model : x86_64 x86_64
% 0.10/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.41 % Memory : 8046.5625MB
% 0.10/0.41 % OS : Linux 6.8.0-71-generic
% 0.10/0.41 % CPULimit : 300
% 0.10/0.41 % WCLimit : 300
% 0.10/0.41 % DateTime : Sun Sep 20 20:10:09 UTC 2026
% 0.10/0.41 % CPUTime :
% 0.10/0.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.46 Running first-order theorem proving
% 0.16/0.46 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
% 0.16/0.50 % Version: 3.5.1
% 0.16/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.50 % Starting sh5l with 300s (1) cores
% 0.16/0.50 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 685800 completed with status 0
% 0.16/0.50 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.50 % No SInE strategy applied
% 0.16/0.50 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.16/0.50 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.50 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 0.16/0.50 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 0.16/0.50 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 0.16/0.50 % U----_043_B31_F1_PI_AE_CS_SP_S2S with pid 685811 completed with status 0
% 0.16/0.50 % Result found by U----_043_B31_F1_PI_AE_CS_SP_S2S
% 0.16/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.50 % No SInE strategy applied
% 0.16/0.50 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.16/0.50 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.50 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 0.16/0.50 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 0.16/0.50 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 0.16/0.50 % Preprocessing time : 0.001 s
% 0.16/0.50
% 0.16/0.50 % Proof found!
% 0.16/0.50 % SZS status Unsatisfiable
% 0.16/0.50 % SZS output start CNFRefutation
% See solution above
% 0.16/0.50 % Parsed axioms : 19
% 0.16/0.50 % Removed by relevancy pruning/SinE : 0
% 0.16/0.50 % Initial clauses : 19
% 0.16/0.50 % Removed in clause preprocessing : 0
% 0.16/0.50 % Initial clauses in saturation : 19
% 0.16/0.50 % Processed clauses : 169
% 0.16/0.50 % ...of these trivial : 50
% 0.16/0.50 % ...subsumed : 46
% 0.16/0.50 % ...remaining for further processing : 73
% 0.16/0.50 % Other redundant clauses eliminated : 0
% 0.16/0.50 % Clauses deleted for lack of memory : 0
% 0.16/0.50 % Backward-subsumed : 0
% 0.16/0.50 % Backward-rewritten : 6
% 0.16/0.50 % Generated clauses : 2139
% 0.16/0.50 % ...of the previous two non-redundant : 1144
% 0.16/0.50 % ...aggressively subsumed : 0
% 0.16/0.50 % Contextual simplify-reflections : 0
% 0.16/0.50 % Paramodulations : 2139
% 0.16/0.50 % Factorizations : 0
% 0.16/0.50 % NegExts : 0
% 0.16/0.50 % Equation resolutions : 0
% 0.16/0.50 % Disequality decompositions : 0
% 0.16/0.50 % Total rewrite steps : 2260
% 0.16/0.50 % ...of those cached : 1522
% 0.16/0.50 % Propositional unsat checks : 0
% 0.16/0.50 % Propositional check models : 0
% 0.16/0.50 % Propositional check unsatisfiable : 0
% 0.16/0.50 % Propositional clauses : 0
% 0.16/0.50 % Propositional clauses after purity: 0
% 0.16/0.50 % Propositional unsat core size : 0
% 0.16/0.50 % Propositional preprocessing time : 0.000
% 0.16/0.50 % Propositional encoding time : 0.000
% 0.16/0.50 % Propositional solver time : 0.000
% 0.16/0.50 % Success case prop preproc time : 0.000
% 0.16/0.50 % Success case prop encoding time : 0.000
% 0.16/0.50 % Success case prop solver time : 0.000
% 0.16/0.50 % Current number of processed clauses : 67
% 0.16/0.50 % Positive orientable unit clauses : 59
% 0.16/0.50 % Positive unorientable unit clauses: 8
% 0.16/0.50 % Negative unit clauses : 0
% 0.16/0.50 % Non-unit-clauses : 0
% 0.16/0.50 % Current number of unprocessed clauses: 994
% 0.16/0.50 % ...number of literals in the above : 994
% 0.16/0.50 % Current number of archived formulas : 0
% 0.16/0.50 % Current number of archived clauses : 6
% 0.16/0.50 % Clause-clause subsumption calls (NU) : 0
% 0.16/0.50 % Rec. Clause-clause subsumption calls : 0
% 0.16/0.50 % Non-unit clause-clause subsumptions : 0
% 0.16/0.50 % Unit Clause-clause subsumption calls : 14
% 0.16/0.50 % Rewrite failures with RHS unbound : 0
% 0.16/0.50 % BW rewrite match attempts : 184
% 0.16/0.50 % BW rewrite match successes : 128
% 0.16/0.50 % Condensation attempts : 0
% 0.16/0.50 % Condensation successes : 0
% 0.16/0.50 % Termbank termtop insertions : 15442
% 0.16/0.50 % Search garbage collected termcells : 2
% 0.16/0.50
% 0.16/0.50 % -------------------------------------------------
% 0.16/0.50 % User time : 0.015 s
% 0.16/0.50 % System time : 0.009 s
% 0.16/0.50 % Total time : 0.023 s
% 0.16/0.50 % Maximum resident set size: 3640 pages
% 0.16/0.50
% 0.16/0.50 % -------------------------------------------------
% 0.16/0.50 % User time : 0.097 s
% 0.16/0.50 % System time : 0.024 s
% 0.16/0.50 % Total time : 0.121 s
% 0.16/0.50 % Maximum resident set size: 4608 pages
% 0.16/0.50 % E exiting
%------------------------------------------------------------------------------