%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP202-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:42:53 PM UTC 2026
% Result : Unsatisfiable 8.03s 1.73s
% Output : CNFRefutation 8.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 5 RR)
% Number of literals : 52 ( 51 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(moufang3,axiom,
multiply(multiply(multiply(X1,X2),X1),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',moufang3) ).
cnf(right_division_multiply,axiom,
right_division(multiply(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_division_multiply) ).
cnf(multiply_right_division,axiom,
multiply(right_division(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_right_division) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
cnf(left_division_multiply,axiom,
left_division(X1,multiply(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_division_multiply) ).
cnf(multiply_left_division,axiom,
multiply(X1,left_division(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_left_division) ).
cnf(prove_moufang1,negated_conjecture,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_moufang1) ).
cnf(c_0_8,axiom,
multiply(X1,identity) = X1,
right_identity ).
cnf(c_0_9,axiom,
multiply(multiply(multiply(X1,X2),X1),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
moufang3 ).
cnf(c_0_10,axiom,
right_division(multiply(X1,X2),X2) = X1,
right_division_multiply ).
cnf(c_0_11,plain,
multiply(multiply(X1,X2),X1) = multiply(X1,multiply(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_8]) ).
cnf(c_0_12,plain,
right_division(multiply(X1,multiply(X2,X1)),X1) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,axiom,
multiply(right_division(X1,X2),X2) = X1,
multiply_right_division ).
cnf(c_0_14,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_15,plain,
right_division(multiply(X1,X2),X1) = multiply(X1,right_division(X2,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
right_division(X1,X1) = identity,
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_17,axiom,
left_division(X1,multiply(X1,X2)) = X2,
left_division_multiply ).
cnf(c_0_18,plain,
multiply(X1,right_division(identity,X1)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_8]),c_0_16]) ).
cnf(c_0_19,plain,
right_division(identity,X1) = left_division(X1,identity),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
multiply(multiply(X1,multiply(X2,X1)),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
inference(rw,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_21,plain,
multiply(left_division(X1,identity),X1) = identity,
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
cnf(c_0_22,plain,
multiply(X1,multiply(left_division(X1,identity),multiply(X1,X2))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_8]) ).
cnf(c_0_23,plain,
multiply(left_division(X1,identity),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_22]),c_0_17]) ).
cnf(c_0_24,plain,
left_division(right_division(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_25,axiom,
multiply(X1,left_division(X1,X2)) = X2,
multiply_left_division ).
cnf(c_0_26,plain,
multiply(X1,multiply(left_division(X1,identity),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_19]) ).
cnf(c_0_27,plain,
multiply(X1,multiply(left_division(X1,X2),X1)) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_11,c_0_25]) ).
cnf(c_0_28,plain,
left_division(left_division(X1,identity),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_29,plain,
multiply(multiply(X1,X2),left_division(X1,identity)) = multiply(X1,multiply(X2,left_division(X1,identity))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_30,plain,
multiply(X1,multiply(multiply(X2,X1),left_division(X1,identity))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_29]),c_0_25]),c_0_8]) ).
cnf(c_0_31,plain,
multiply(multiply(X1,X2),left_division(X2,identity)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_30]),c_0_23]) ).
cnf(c_0_32,plain,
multiply(left_division(X1,identity),X2) = left_division(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_25]) ).
cnf(c_0_33,plain,
multiply(left_division(multiply(X1,X2),identity),X1) = left_division(X2,identity),
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
cnf(c_0_34,plain,
right_division(X1,multiply(X2,X1)) = left_division(X2,identity),
inference(spm,[status(thm)],[c_0_10,c_0_23]) ).
cnf(c_0_35,plain,
multiply(multiply(X1,left_division(X2,identity)),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_30]),c_0_26]),c_0_28]),c_0_8]) ).
cnf(c_0_36,plain,
left_division(multiply(X1,X2),X1) = left_division(X2,identity),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
right_division(X1,X2) = left_division(multiply(X2,left_division(X1,identity)),identity),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
left_division(multiply(X1,X2),identity) = multiply(left_division(X2,identity),left_division(X1,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_23]),c_0_32]) ).
cnf(c_0_39,plain,
multiply(multiply(X1,multiply(X2,multiply(X1,left_division(X3,identity)))),X3) = multiply(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_35,c_0_20]) ).
cnf(c_0_40,plain,
multiply(left_division(right_division(X1,X2),identity),X1) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_41,plain,
right_division(X1,X2) = multiply(X1,left_division(X2,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_28]),c_0_8]) ).
cnf(c_0_42,negated_conjecture,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
inference(fof_simplification,[status(thm)],[prove_moufang1]) ).
cnf(c_0_43,plain,
multiply(multiply(multiply(X1,X2),multiply(X3,X1)),X2) = multiply(multiply(X1,X2),multiply(X3,multiply(X1,X2))),
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)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_38]),c_0_28]),c_0_8]),c_0_28]),c_0_8]),c_0_41]),c_0_38]),c_0_28]),c_0_8]),c_0_28]),c_0_8]),c_0_41]),c_0_38]),c_0_28]),c_0_8]),c_0_28]),c_0_8]) ).
cnf(c_0_44,plain,
left_division(left_division(X1,X2),identity) = multiply(left_division(X2,identity),X1),
inference(spm,[status(thm)],[c_0_33,c_0_25]) ).
cnf(c_0_45,negated_conjecture,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
c_0_42 ).
cnf(c_0_46,plain,
multiply(multiply(X1,multiply(X2,X3)),left_division(X3,X1)) = multiply(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_43,c_0_25]) ).
cnf(c_0_47,plain,
left_division(left_division(X1,X2),X3) = multiply(multiply(left_division(X2,identity),X1),X3),
inference(spm,[status(thm)],[c_0_32,c_0_44]) ).
cnf(c_0_48,plain,
left_division(X1,X1) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_8]) ).
cnf(c_0_49,negated_conjecture,
multiply(multiply(a,b),multiply(c,a)) != multiply(a,multiply(multiply(b,c),a)),
inference(rw,[status(thm)],[c_0_45,c_0_11]) ).
cnf(c_0_50,plain,
multiply(multiply(X1,X2),multiply(X3,X1)) = multiply(X1,multiply(multiply(X2,X3),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_31]),c_0_47]),c_0_48]),c_0_14]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP202-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.47 % Computer : n006.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 20:05:42 UTC 2026
% 0.19/0.48 % CPUTime :
% 0.19/0.48 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.53 Running first-order theorem proving
% 0.24/0.53 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
% 8.03/1.73 % Version: 3.5.1
% 8.03/1.73 % Preprocessing class: FSSSSMSSSSSNFFN.
% 8.03/1.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.03/1.73 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 8.03/1.73 % Starting new_bool_3 with 300s (1) cores
% 8.03/1.73 % Starting new_bool_1 with 300s (1) cores
% 8.03/1.73 % Starting sh5l with 300s (1) cores
% 8.03/1.73 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1147333 completed with status 0
% 8.03/1.73 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 8.03/1.73 % Preprocessing class: FSSSSMSSSSSNFFN.
% 8.03/1.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.03/1.73 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 8.03/1.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.03/1.73 % No SInE strategy applied
% 8.03/1.73 % Search class: FUUPM-FFSF21-MFFFFFNN
% 8.03/1.73 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 8.03/1.73 % Starting SubtermCWHack with 136s (1) cores
% 8.03/1.73 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 8.03/1.73 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 8.03/1.73 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 8.03/1.73 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 8.03/1.73 % H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with pid 1147339 completed with status 0
% 8.03/1.73 % Result found by H----_047_B31_F1_PI_AE_R4_CS_SP_S2S
% 8.03/1.73 % Preprocessing class: FSSSSMSSSSSNFFN.
% 8.03/1.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.03/1.73 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 8.03/1.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.03/1.73 % No SInE strategy applied
% 8.03/1.73 % Search class: FUUPM-FFSF21-MFFFFFNN
% 8.03/1.73 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 8.03/1.73 % Starting SubtermCWHack with 136s (1) cores
% 8.03/1.73 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 8.03/1.73 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 8.03/1.73 % Preprocessing time : 0.001 s
% 8.03/1.73
% 8.03/1.73 % Proof found!
% 8.03/1.73 % SZS status Unsatisfiable
% 8.03/1.73 % SZS output start CNFRefutation
% See solution above
% 8.03/1.73 % Parsed axioms : 10
% 8.03/1.73 % Removed by relevancy pruning/SinE : 0
% 8.03/1.73 % Initial clauses : 10
% 8.03/1.73 % Removed in clause preprocessing : 0
% 8.03/1.73 % Initial clauses in saturation : 10
% 8.03/1.73 % Processed clauses : 692
% 8.03/1.73 % ...of these trivial : 224
% 8.03/1.73 % ...subsumed : 217
% 8.03/1.73 % ...remaining for further processing : 251
% 8.03/1.73 % Other redundant clauses eliminated : 0
% 8.03/1.73 % Clauses deleted for lack of memory : 0
% 8.03/1.73 % Backward-subsumed : 0
% 8.03/1.73 % Backward-rewritten : 100
% 8.03/1.73 % Generated clauses : 31210
% 8.03/1.73 % ...of the previous two non-redundant : 23356
% 8.03/1.73 % ...aggressively subsumed : 0
% 8.03/1.73 % Contextual simplify-reflections : 0
% 8.03/1.73 % Paramodulations : 31210
% 8.03/1.73 % Factorizations : 0
% 8.03/1.73 % NegExts : 0
% 8.03/1.73 % Equation resolutions : 0
% 8.03/1.73 % Disequality decompositions : 0
% 8.03/1.73 % Total rewrite steps : 142439
% 8.03/1.73 % ...of those cached : 131508
% 8.03/1.73 % Propositional unsat checks : 0
% 8.03/1.73 % Propositional check models : 0
% 8.03/1.73 % Propositional check unsatisfiable : 0
% 8.03/1.73 % Propositional clauses : 0
% 8.03/1.73 % Propositional clauses after purity: 0
% 8.03/1.73 % Propositional unsat core size : 0
% 8.03/1.73 % Propositional preprocessing time : 0.000
% 8.03/1.73 % Propositional encoding time : 0.000
% 8.03/1.73 % Propositional solver time : 0.000
% 8.03/1.73 % Success case prop preproc time : 0.000
% 8.03/1.73 % Success case prop encoding time : 0.000
% 8.03/1.73 % Success case prop solver time : 0.000
% 8.03/1.73 % Current number of processed clauses : 151
% 8.03/1.73 % Positive orientable unit clauses : 139
% 8.03/1.73 % Positive unorientable unit clauses: 12
% 8.03/1.73 % Negative unit clauses : 0
% 8.03/1.73 % Non-unit-clauses : 0
% 8.03/1.73 % Current number of unprocessed clauses: 21908
% 8.03/1.73 % ...number of literals in the above : 21908
% 8.03/1.73 % Current number of archived formulas : 0
% 8.03/1.73 % Current number of archived clauses : 100
% 8.03/1.73 % Clause-clause subsumption calls (NU) : 0
% 8.03/1.73 % Rec. Clause-clause subsumption calls : 0
% 8.03/1.73 % Non-unit clause-clause subsumptions : 0
% 8.03/1.73 % Unit Clause-clause subsumption calls : 209
% 8.03/1.73 % Rewrite failures with RHS unbound : 41
% 8.03/1.73 % BW rewrite match attempts : 1635
% 8.03/1.73 % BW rewrite match successes : 305
% 8.03/1.73 % Condensation attempts : 0
% 8.03/1.73 % Condensation successes : 0
% 8.03/1.73 % Termbank termtop insertions : 761778
% 8.03/1.73 % Search garbage collected termcells : 2
% 8.03/1.73
% 8.03/1.73 % -------------------------------------------------
% 8.03/1.73 % User time : 1.044 s
% 8.03/1.73 % System time : 0.033 s
% 8.03/1.73 % Total time : 1.078 s
% 8.03/1.73 % Maximum resident set size: 3632 pages
% 8.03/1.73
% 8.03/1.73 % -------------------------------------------------
% 8.03/1.73 % User time : 5.238 s
% 8.03/1.73 % System time : 0.254 s
% 8.03/1.73 % Total time : 5.492 s
% 8.03/1.73 % Maximum resident set size: 4608 pages
% 8.03/1.73 % E exiting
%------------------------------------------------------------------------------