%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP185-1 : 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 0.30s 0.70s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 6 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 : 61 ( 5 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(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/sandbox2/benchmark/theBenchmark.p',prove_p22a) ).
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(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(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(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(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(idempotence_of_lub,axiom,
least_upper_bound(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_of_lub) ).
cnf(c_0_12,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_13,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_14,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_15,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_16,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
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_15 ).
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,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_23,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_16]) ).
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_14]),c_0_20]),c_0_14]),c_0_21]),c_0_21]),c_0_19]),c_0_20]),c_0_14]),c_0_20]),c_0_14]),c_0_21]) ).
cnf(c_0_27,plain,
multiply(X1,identity) = X1,
inference(rw,[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
% 0.00/0.05 % Problem : GRP185-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.47 % Computer : n011.cluster.edu
% 0.19/0.47 % Model : x86_64 x86_64
% 0.19/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.47 % Memory : 8046.5625MB
% 0.19/0.47 % OS : Linux 6.8.0-71-generic
% 0.19/0.47 % CPULimit : 300
% 0.19/0.47 % WCLimit : 300
% 0.19/0.47 % DateTime : Sun Sep 20 20:04:55 UTC 2026
% 0.19/0.48 % CPUTime :
% 0.19/0.48 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.56 Running first-order theorem proving
% 0.24/0.56 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
% 0.30/0.70 % Version: 3.5.1
% 0.30/0.70 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.30/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.30/0.70 % Starting new_bool_3 with 300s (1) cores
% 0.30/0.70 % Starting new_bool_1 with 300s (1) cores
% 0.30/0.70 % Starting sh5l with 300s (1) cores
% 0.30/0.70 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 53359 completed with status 0
% 0.30/0.70 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.30/0.70 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.30/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.30/0.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.30/0.70 % No SInE strategy applied
% 0.30/0.70 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.30/0.70 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.30/0.70 % Starting SubtermCWHack with 136s (1) cores
% 0.30/0.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.30/0.70 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 0.30/0.70 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 0.30/0.70 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 0.30/0.70 % U----_043_B31_F1_PI_AE_CS_SP_S2S with pid 53370 completed with status 0
% 0.30/0.70 % Result found by U----_043_B31_F1_PI_AE_CS_SP_S2S
% 0.30/0.70 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.30/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.30/0.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.30/0.70 % No SInE strategy applied
% 0.30/0.70 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.30/0.70 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.30/0.70 % Starting SubtermCWHack with 136s (1) cores
% 0.30/0.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.30/0.70 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 0.30/0.70 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 0.30/0.70 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 0.30/0.70 % Preprocessing time : 0.002 s
% 0.30/0.70
% 0.30/0.70 % Proof found!
% 0.30/0.70 % SZS status Unsatisfiable
% 0.30/0.70 % SZS output start CNFRefutation
% See solution above
% 0.30/0.70 % Parsed axioms : 16
% 0.30/0.70 % Removed by relevancy pruning/SinE : 0
% 0.30/0.70 % Initial clauses : 16
% 0.30/0.70 % Removed in clause preprocessing : 0
% 0.30/0.70 % Initial clauses in saturation : 16
% 0.30/0.70 % Processed clauses : 169
% 0.30/0.70 % ...of these trivial : 49
% 0.30/0.70 % ...subsumed : 46
% 0.30/0.70 % ...remaining for further processing : 74
% 0.30/0.70 % Other redundant clauses eliminated : 0
% 0.30/0.70 % Clauses deleted for lack of memory : 0
% 0.30/0.70 % Backward-subsumed : 0
% 0.30/0.70 % Backward-rewritten : 8
% 0.30/0.70 % Generated clauses : 2122
% 0.30/0.70 % ...of the previous two non-redundant : 1138
% 0.30/0.70 % ...aggressively subsumed : 0
% 0.30/0.70 % Contextual simplify-reflections : 0
% 0.30/0.70 % Paramodulations : 2122
% 0.30/0.70 % Factorizations : 0
% 0.30/0.70 % NegExts : 0
% 0.30/0.70 % Equation resolutions : 0
% 0.30/0.70 % Disequality decompositions : 0
% 0.30/0.70 % Total rewrite steps : 2179
% 0.30/0.70 % ...of those cached : 1470
% 0.30/0.70 % Propositional unsat checks : 0
% 0.30/0.70 % Propositional check models : 0
% 0.30/0.70 % Propositional check unsatisfiable : 0
% 0.30/0.70 % Propositional clauses : 0
% 0.30/0.70 % Propositional clauses after purity: 0
% 0.30/0.70 % Propositional unsat core size : 0
% 0.30/0.70 % Propositional preprocessing time : 0.000
% 0.30/0.70 % Propositional encoding time : 0.000
% 0.30/0.70 % Propositional solver time : 0.000
% 0.30/0.70 % Success case prop preproc time : 0.000
% 0.30/0.70 % Success case prop encoding time : 0.000
% 0.30/0.70 % Success case prop solver time : 0.000
% 0.30/0.70 % Current number of processed clauses : 66
% 0.30/0.70 % Positive orientable unit clauses : 58
% 0.30/0.70 % Positive unorientable unit clauses: 8
% 0.30/0.70 % Negative unit clauses : 0
% 0.30/0.70 % Non-unit-clauses : 0
% 0.30/0.70 % Current number of unprocessed clauses: 980
% 0.30/0.70 % ...number of literals in the above : 980
% 0.30/0.70 % Current number of archived formulas : 0
% 0.30/0.70 % Current number of archived clauses : 8
% 0.30/0.70 % Clause-clause subsumption calls (NU) : 0
% 0.30/0.70 % Rec. Clause-clause subsumption calls : 0
% 0.30/0.70 % Non-unit clause-clause subsumptions : 0
% 0.30/0.70 % Unit Clause-clause subsumption calls : 14
% 0.30/0.70 % Rewrite failures with RHS unbound : 0
% 0.30/0.70 % BW rewrite match attempts : 170
% 0.30/0.70 % BW rewrite match successes : 126
% 0.30/0.70 % Condensation attempts : 0
% 0.30/0.70 % Condensation successes : 0
% 0.30/0.70 % Termbank termtop insertions : 15118
% 0.30/0.70 % Search garbage collected termcells : 2
% 0.30/0.70
% 0.30/0.70 % -------------------------------------------------
% 0.30/0.70 % User time : 0.029 s
% 0.30/0.70 % System time : 0.010 s
% 0.30/0.70 % Total time : 0.039 s
% 0.30/0.70 % Maximum resident set size: 3384 pages
% 0.30/0.70
% 0.30/0.70 % -------------------------------------------------
% 0.30/0.70 % User time : 0.300 s
% 0.30/0.70 % System time : 0.036 s
% 0.30/0.70 % Total time : 0.336 s
% 0.30/0.70 % Maximum resident set size: 4608 pages
% 0.30/0.70 % E exiting
%------------------------------------------------------------------------------