%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP201-1 : 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 : n012.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 12:38:58 PM UTC 2026
% Result : Unsatisfiable 4.47s 6.07s
% Output : CNFRefutation 4.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of clauses : 57 ( 57 unt; 0 nHn; 5 RR)
% Number of literals : 57 ( 56 equ; 4 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; 4 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(moufang2,axiom,
multiply(multiply(multiply(X1,X2),X3),X2) = multiply(X1,multiply(X2,multiply(X3,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',moufang2) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
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(right_identity,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_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_moufang3,negated_conjecture,
multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_moufang3) ).
cnf(c_0_8,axiom,
multiply(multiply(multiply(X1,X2),X3),X2) = multiply(X1,multiply(X2,multiply(X3,X2))),
moufang2 ).
cnf(c_0_9,axiom,
multiply(identity,X1) = X1,
left_identity ).
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_9]) ).
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,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_15,axiom,
multiply(X1,identity) = X1,
right_identity ).
cnf(c_0_16,plain,
right_division(X1,X1) = identity,
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
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_14,c_0_15]),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,
right_division(multiply(X1,multiply(X2,multiply(X3,X2))),X2) = multiply(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
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,axiom,
multiply(X1,left_division(X1,X2)) = X2,
multiply_left_division ).
cnf(c_0_23,plain,
multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_20]),c_0_14]),c_0_10]) ).
cnf(c_0_24,plain,
multiply(multiply(X1,X2),left_division(X2,identity)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_15]),c_0_10]) ).
cnf(c_0_25,plain,
multiply(X1,multiply(X1,left_division(multiply(X1,X1),X2))) = X2,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
left_division(multiply(X1,X2),X1) = left_division(X2,identity),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_27,plain,
multiply(X1,left_division(multiply(X1,X1),X2)) = left_division(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_28,plain,
left_division(left_division(X1,X2),identity) = left_division(X2,X1),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_29,plain,
left_division(multiply(X1,X1),X2) = left_division(X1,left_division(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).
cnf(c_0_30,plain,
left_division(left_division(X1,X2),X1) = left_division(X2,multiply(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_28]) ).
cnf(c_0_31,plain,
multiply(multiply(X1,multiply(X2,X1)),X2) = multiply(X1,multiply(X2,multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_32,plain,
multiply(X1,multiply(left_division(X1,X2),X1)) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_11,c_0_22]) ).
cnf(c_0_33,plain,
left_division(multiply(X1,X2),multiply(X1,X1)) = left_division(X2,X1),
inference(spm,[status(thm)],[c_0_30,c_0_17]) ).
cnf(c_0_34,plain,
multiply(X1,multiply(left_division(X1,X2),X2)) = multiply(multiply(X2,X1),left_division(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_22]) ).
cnf(c_0_35,plain,
multiply(multiply(X1,X2),left_division(X2,X1)) = multiply(X1,X1),
inference(spm,[status(thm)],[c_0_22,c_0_33]) ).
cnf(c_0_36,plain,
multiply(X1,multiply(left_division(X1,X2),X2)) = multiply(X2,X2),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,plain,
left_division(X1,multiply(X2,X2)) = multiply(left_division(X1,X2),X2),
inference(spm,[status(thm)],[c_0_17,c_0_36]) ).
cnf(c_0_38,plain,
multiply(left_division(X1,identity),X2) = left_division(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_37]),c_0_26]) ).
cnf(c_0_39,plain,
multiply(left_division(X1,identity),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_17,c_0_38]) ).
cnf(c_0_40,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_26,c_0_39]),c_0_38]) ).
cnf(c_0_41,plain,
left_division(multiply(X1,X2),X3) = multiply(multiply(left_division(X2,identity),left_division(X1,identity)),X3),
inference(spm,[status(thm)],[c_0_38,c_0_40]) ).
cnf(c_0_42,plain,
right_division(X1,X2) = multiply(X1,left_division(X2,identity)),
inference(spm,[status(thm)],[c_0_24,c_0_13]) ).
cnf(c_0_43,plain,
multiply(X1,multiply(left_division(X1,identity),X2)) = X2,
inference(spm,[status(thm)],[c_0_22,c_0_38]) ).
cnf(c_0_44,plain,
multiply(X1,multiply(X2,multiply(multiply(multiply(left_division(X2,identity),left_division(X1,identity)),X3),X2))) = multiply(X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_22]),c_0_41]) ).
cnf(c_0_45,plain,
left_division(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_22]) ).
cnf(c_0_46,plain,
multiply(multiply(X1,X2),left_division(X1,identity)) = multiply(X1,multiply(X2,left_division(X1,identity))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_42]),c_0_42]) ).
cnf(c_0_47,negated_conjecture,
multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))),
inference(fof_simplification,[status(thm)],[prove_moufang3]) ).
cnf(c_0_48,plain,
multiply(X1,multiply(multiply(multiply(left_division(X1,identity),X2),X3),X1)) = multiply(X2,multiply(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_28]),c_0_45]) ).
cnf(c_0_49,plain,
multiply(X1,multiply(left_division(X1,X2),left_division(X1,identity))) = multiply(X2,left_division(X1,identity)),
inference(spm,[status(thm)],[c_0_46,c_0_22]) ).
cnf(c_0_50,plain,
left_division(left_division(X1,X2),X3) = multiply(left_division(X2,X1),X3),
inference(spm,[status(thm)],[c_0_38,c_0_28]) ).
cnf(c_0_51,negated_conjecture,
multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))),
c_0_47 ).
cnf(c_0_52,plain,
multiply(multiply(X1,multiply(X2,X1)),multiply(X3,X1)) = multiply(X1,multiply(X2,multiply(X1,multiply(X3,X1)))),
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_48,c_0_49]),c_0_28]),c_0_45]),c_0_8]),c_0_50]),c_0_45]),c_0_28]),c_0_45]),c_0_11]) ).
cnf(c_0_53,plain,
multiply(multiply(X1,left_division(X2,identity)),X2) = X1,
inference(rw,[status(thm)],[c_0_13,c_0_42]) ).
cnf(c_0_54,negated_conjecture,
multiply(multiply(a,multiply(b,a)),c) != multiply(a,multiply(b,multiply(a,c))),
inference(rw,[status(thm)],[c_0_51,c_0_11]) ).
cnf(c_0_55,plain,
multiply(multiply(X1,multiply(X2,X1)),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP201-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/5.36 % Computer : n012.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sun Sep 20 20:05:57 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.40 Running first-order theorem proving
% 0.13/5.40 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
% 4.47/6.07 % Version: 3.5.1
% 4.47/6.07 % Preprocessing class: FSSSSMSSSSSNFFN.
% 4.47/6.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.47/6.07 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 4.47/6.07 % Starting new_bool_3 with 300s (1) cores
% 4.47/6.07 % Starting new_bool_1 with 300s (1) cores
% 4.47/6.07 % Starting sh5l with 300s (1) cores
% 4.47/6.07 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 757129 completed with status 0
% 4.47/6.07 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 4.47/6.07 % Preprocessing class: FSSSSMSSSSSNFFN.
% 4.47/6.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.47/6.07 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 4.47/6.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.47/6.07 % No SInE strategy applied
% 4.47/6.07 % Search class: FUUPM-FFSF21-MFFFFFNN
% 4.47/6.07 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 4.47/6.07 % Starting SubtermCWHack with 136s (1) cores
% 4.47/6.07 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 4.47/6.07 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 4.47/6.07 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 4.47/6.07 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 4.47/6.07 % H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with pid 757135 completed with status 0
% 4.47/6.07 % Result found by H----_047_B31_F1_PI_AE_R4_CS_SP_S2S
% 4.47/6.07 % Preprocessing class: FSSSSMSSSSSNFFN.
% 4.47/6.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.47/6.07 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 4.47/6.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.47/6.07 % No SInE strategy applied
% 4.47/6.07 % Search class: FUUPM-FFSF21-MFFFFFNN
% 4.47/6.07 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 4.47/6.07 % Starting SubtermCWHack with 136s (1) cores
% 4.47/6.07 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 4.47/6.07 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 4.47/6.07 % Preprocessing time : 0.001 s
% 4.47/6.07
% 4.47/6.07 % Proof found!
% 4.47/6.07 % SZS status Unsatisfiable
% 4.47/6.07 % SZS output start CNFRefutation
% See solution above
% 4.47/6.07 % Parsed axioms : 10
% 4.47/6.07 % Removed by relevancy pruning/SinE : 0
% 4.47/6.07 % Initial clauses : 10
% 4.47/6.07 % Removed in clause preprocessing : 0
% 4.47/6.07 % Initial clauses in saturation : 10
% 4.47/6.07 % Processed clauses : 644
% 4.47/6.07 % ...of these trivial : 194
% 4.47/6.07 % ...subsumed : 209
% 4.47/6.07 % ...remaining for further processing : 241
% 4.47/6.07 % Other redundant clauses eliminated : 0
% 4.47/6.07 % Clauses deleted for lack of memory : 0
% 4.47/6.07 % Backward-subsumed : 0
% 4.47/6.07 % Backward-rewritten : 78
% 4.47/6.07 % Generated clauses : 34563
% 4.47/6.07 % ...of the previous two non-redundant : 26057
% 4.47/6.07 % ...aggressively subsumed : 0
% 4.47/6.07 % Contextual simplify-reflections : 0
% 4.47/6.07 % Paramodulations : 34563
% 4.47/6.07 % Factorizations : 0
% 4.47/6.07 % NegExts : 0
% 4.47/6.07 % Equation resolutions : 0
% 4.47/6.07 % Disequality decompositions : 0
% 4.47/6.07 % Total rewrite steps : 140558
% 4.47/6.07 % ...of those cached : 131723
% 4.47/6.07 % Propositional unsat checks : 0
% 4.47/6.07 % Propositional check models : 0
% 4.47/6.07 % Propositional check unsatisfiable : 0
% 4.47/6.07 % Propositional clauses : 0
% 4.47/6.07 % Propositional clauses after purity: 0
% 4.47/6.07 % Propositional unsat core size : 0
% 4.47/6.07 % Propositional preprocessing time : 0.000
% 4.47/6.07 % Propositional encoding time : 0.000
% 4.47/6.07 % Propositional solver time : 0.000
% 4.47/6.07 % Success case prop preproc time : 0.000
% 4.47/6.07 % Success case prop encoding time : 0.000
% 4.47/6.07 % Success case prop solver time : 0.000
% 4.47/6.07 % Current number of processed clauses : 163
% 4.47/6.07 % Positive orientable unit clauses : 149
% 4.47/6.07 % Positive unorientable unit clauses: 14
% 4.47/6.07 % Negative unit clauses : 0
% 4.47/6.07 % Non-unit-clauses : 0
% 4.47/6.07 % Current number of unprocessed clauses: 25023
% 4.47/6.07 % ...number of literals in the above : 25023
% 4.47/6.07 % Current number of archived formulas : 0
% 4.47/6.07 % Current number of archived clauses : 78
% 4.47/6.07 % Clause-clause subsumption calls (NU) : 0
% 4.47/6.07 % Rec. Clause-clause subsumption calls : 0
% 4.47/6.07 % Non-unit clause-clause subsumptions : 0
% 4.47/6.07 % Unit Clause-clause subsumption calls : 95
% 4.47/6.07 % Rewrite failures with RHS unbound : 53
% 4.47/6.07 % BW rewrite match attempts : 1706
% 4.47/6.07 % BW rewrite match successes : 115
% 4.47/6.07 % Condensation attempts : 0
% 4.47/6.07 % Condensation successes : 0
% 4.47/6.07 % Termbank termtop insertions : 763451
% 4.47/6.07 % Search garbage collected termcells : 2
% 4.47/6.07
% 4.47/6.07 % -------------------------------------------------
% 4.47/6.07 % User time : 0.592 s
% 4.47/6.07 % System time : 0.031 s
% 4.47/6.07 % Total time : 0.623 s
% 4.47/6.07 % Maximum resident set size: 3632 pages
% 4.47/6.07
% 4.47/6.07 % -------------------------------------------------
% 4.47/6.07 % User time : 2.953 s
% 4.47/6.07 % System time : 0.159 s
% 4.47/6.07 % Total time : 3.111 s
% 4.47/6.07 % Maximum resident set size: 4608 pages
% 4.47/6.07 % E exiting
%------------------------------------------------------------------------------