%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP655-12 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:40:37 PM UTC 2026
% Result : Unsatisfiable 15.17s 7.63s
% Output : CNFRefutation 15.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of clauses : 58 ( 58 unt; 0 nHn; 4 RR)
% Number of literals : 58 ( 57 equ; 3 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f04,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
cnf(f05,axiom,
mult(X1,mult(X2,mult(X3,X2))) = mult(mult(mult(X1,X2),X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
cnf(f03,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
cnf(f01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
cnf(f02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
cnf(goal,negated_conjecture,
mult(rd(x1,x1),x0) != x0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c_0_6,axiom,
rd(mult(X1,X2),X2) = X1,
f04 ).
cnf(c_0_7,axiom,
mult(X1,mult(X2,mult(X3,X2))) = mult(mult(mult(X1,X2),X3),X2),
f05 ).
cnf(c_0_8,axiom,
mult(rd(X1,X2),X2) = X1,
f03 ).
cnf(c_0_9,plain,
rd(mult(X1,mult(X2,mult(X3,X2))),X2) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
mult(rd(X1,X2),mult(X2,mult(X3,X2))) = mult(mult(X1,X3),X2),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
rd(mult(X1,mult(X2,X3)),X2) = mult(mult(X1,X2),rd(X3,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_12,axiom,
mult(X1,ld(X1,X2)) = X2,
f01 ).
cnf(c_0_13,plain,
rd(mult(mult(X1,X2),X3),mult(X3,mult(X2,X3))) = rd(X1,X3),
inference(spm,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_14,plain,
mult(mult(X1,X2),rd(ld(X2,X3),X2)) = rd(mult(X1,X3),X2),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
rd(mult(X1,X2),mult(X2,mult(X3,X2))) = rd(rd(X1,X3),X2),
inference(spm,[status(thm)],[c_0_13,c_0_8]) ).
cnf(c_0_16,plain,
rd(mult(rd(X1,X2),X3),X2) = mult(X1,rd(ld(X2,X3),X2)),
inference(spm,[status(thm)],[c_0_14,c_0_8]) ).
cnf(c_0_17,plain,
rd(rd(X1,rd(X2,X3)),X3) = rd(mult(X1,X3),mult(X3,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_8]) ).
cnf(c_0_18,plain,
mult(X1,rd(ld(X2,X2),X2)) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_6,c_0_16]) ).
cnf(c_0_19,axiom,
ld(X1,mult(X1,X2)) = X2,
f02 ).
cnf(c_0_20,plain,
mult(rd(mult(X1,X2),mult(X2,X3)),X2) = rd(X1,rd(X3,X2)),
inference(spm,[status(thm)],[c_0_8,c_0_17]) ).
cnf(c_0_21,plain,
rd(rd(X1,rd(ld(X2,X2),X2)),X2) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_18]) ).
cnf(c_0_22,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_8]) ).
cnf(c_0_23,plain,
rd(X1,rd(ld(X2,X3),X2)) = mult(rd(mult(X1,X2),X3),X2),
inference(spm,[status(thm)],[c_0_20,c_0_12]) ).
cnf(c_0_24,plain,
ld(X1,rd(X1,X2)) = rd(ld(X2,X2),X2),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_25,plain,
rd(X1,rd(ld(X2,X2),X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_8,c_0_21]) ).
cnf(c_0_26,plain,
ld(mult(rd(mult(X1,X2),X3),X2),X1) = rd(ld(X2,X3),X2),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
mult(X1,ld(X2,rd(X2,X3))) = rd(X1,X3),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_28,plain,
rd(rd(rd(X1,X2),X3),X2) = rd(X1,mult(X2,mult(X3,X2))),
inference(spm,[status(thm)],[c_0_15,c_0_8]) ).
cnf(c_0_29,plain,
rd(X1,ld(X2,rd(X2,X3))) = mult(X1,X3),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_30,plain,
mult(ld(X1,rd(X1,X2)),X2) = ld(X2,X2),
inference(spm,[status(thm)],[c_0_8,c_0_24]) ).
cnf(c_0_31,plain,
mult(ld(ld(X1,rd(X1,X2)),X3),X2) = mult(X2,mult(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_27]),c_0_28]),c_0_22]),c_0_29]) ).
cnf(c_0_32,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_12]) ).
cnf(c_0_33,plain,
ld(X1,X1) = rd(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_8]),c_0_27]) ).
cnf(c_0_34,plain,
rd(X1,ld(X2,X3)) = mult(X1,ld(X3,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_35,plain,
mult(X1,rd(X1,X1)) = 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(spm,[status(thm)],[c_0_31,c_0_33]),c_0_34]),c_0_22]),c_0_30]),c_0_33]),c_0_8]),c_0_30]),c_0_33]) ).
cnf(c_0_36,plain,
rd(X1,rd(rd(X2,X2),X2)) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_33]),c_0_6]) ).
cnf(c_0_37,plain,
ld(ld(X1,rd(X1,X2)),ld(X1,rd(X1,X2))) = rd(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_30]),c_0_34]),c_0_22]),c_0_19]) ).
cnf(c_0_38,plain,
mult(mult(X1,rd(X2,X3)),rd(X3,rd(X2,X3))) = rd(mult(X1,X2),rd(X2,X3)),
inference(spm,[status(thm)],[c_0_11,c_0_8]) ).
cnf(c_0_39,plain,
mult(rd(rd(X1,X1),X1),rd(X1,X1)) = rd(rd(X1,X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_8]) ).
cnf(c_0_40,plain,
rd(X1,rd(X2,X2)) = mult(X1,rd(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_37]),c_0_37]) ).
cnf(c_0_41,plain,
mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
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_38,c_0_39]),c_0_40]),c_0_35]),c_0_8]),c_0_8]),c_0_40]) ).
cnf(c_0_42,plain,
rd(rd(X1,X2),rd(X3,X2)) = mult(rd(X1,mult(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_20,c_0_8]) ).
cnf(c_0_43,plain,
mult(mult(rd(X1,mult(X2,X1)),X2),mult(rd(X1,mult(X2,X1)),X2)) = mult(rd(X1,mult(X2,X1)),X2),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_44,plain,
mult(mult(rd(X1,X2),rd(X2,X1)),mult(rd(X1,X2),rd(X2,X1))) = mult(rd(X1,X2),rd(X2,X1)),
inference(spm,[status(thm)],[c_0_43,c_0_8]) ).
cnf(c_0_45,plain,
mult(mult(X1,rd(X2,mult(X1,X2))),mult(X1,rd(X2,mult(X1,X2)))) = mult(X1,rd(X2,mult(X1,X2))),
inference(spm,[status(thm)],[c_0_44,c_0_6]) ).
cnf(c_0_46,plain,
mult(mult(X1,ld(X2,X3)),ld(X3,X2)) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_34]) ).
cnf(c_0_47,plain,
mult(mult(X1,rd(rd(X2,X2),X1)),mult(X1,rd(rd(X2,X2),X1))) = mult(X1,rd(rd(X2,X2),X1)),
inference(spm,[status(thm)],[c_0_45,c_0_15]) ).
cnf(c_0_48,plain,
mult(mult(X1,rd(X2,X2)),rd(X2,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_37]),c_0_37]) ).
cnf(c_0_49,plain,
mult(mult(rd(X1,X1),mult(rd(X2,X2),rd(X1,X1))),mult(rd(X1,X1),mult(rd(X2,X2),rd(X1,X1)))) = mult(rd(X1,X1),mult(rd(X2,X2),rd(X1,X1))),
inference(spm,[status(thm)],[c_0_47,c_0_40]) ).
cnf(c_0_50,plain,
mult(mult(rd(X1,X1),mult(X2,rd(X1,X1))),rd(X1,X1)) = ld(rd(X1,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_31]),c_0_40]),c_0_19]) ).
cnf(c_0_51,plain,
mult(rd(X1,mult(ld(X2,X1),X3)),ld(X2,X1)) = rd(X2,mult(X3,ld(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_12]),c_0_34]) ).
cnf(c_0_52,plain,
mult(ld(rd(X1,X1),rd(X2,X2)),rd(X2,X2)) = ld(rd(X1,X1),rd(X2,X2)),
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_11,c_0_49]),c_0_40]),c_0_50]),c_0_50]),c_0_40]),c_0_48]) ).
cnf(c_0_53,negated_conjecture,
mult(rd(x1,x1),x0) != x0,
inference(fof_simplification,[status(thm)],[goal]) ).
cnf(c_0_54,plain,
rd(X1,X1) = rd(X2,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(spm,[status(thm)],[c_0_51,c_0_52]),c_0_34]),c_0_12]),c_0_12]),c_0_12]),c_0_40]),c_0_41]) ).
cnf(c_0_55,negated_conjecture,
mult(rd(x1,x1),x0) != x0,
c_0_53 ).
cnf(c_0_56,plain,
mult(rd(X1,X1),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_54]),c_0_40]),c_0_35]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP655-12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.37 % Computer : n010.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Sun Sep 20 20:29:46 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.41 Running first-order theorem proving
% 0.15/5.41 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
% 15.17/7.63 % Version: 3.5.1
% 15.17/7.63 % Preprocessing class: FSSSSMSSSSSNFFN.
% 15.17/7.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.17/7.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 15.17/7.63 % Starting new_bool_3 with 300s (1) cores
% 15.17/7.63 % Starting new_bool_1 with 300s (1) cores
% 15.17/7.63 % Starting sh5l with 300s (1) cores
% 15.17/7.63 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3467195 completed with status 0
% 15.17/7.63 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 15.17/7.63 % Preprocessing class: FSSSSMSSSSSNFFN.
% 15.17/7.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.17/7.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 15.17/7.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 15.17/7.63 % No SInE strategy applied
% 15.17/7.63 % Search class: FUUPM-FFSF22-MFFFFFNN
% 15.17/7.63 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 15.17/7.63 % Starting SubtermCWHack with 136s (1) cores
% 15.17/7.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 15.17/7.63 % Starting E---G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 15.17/7.63 % Starting U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 15.17/7.63 % Starting U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 15.17/7.63 % U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 3467204 completed with status 0
% 15.17/7.63 % Result found by U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 15.17/7.63 % Preprocessing class: FSSSSMSSSSSNFFN.
% 15.17/7.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.17/7.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 15.17/7.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 15.17/7.63 % No SInE strategy applied
% 15.17/7.63 % Search class: FUUPM-FFSF22-MFFFFFNN
% 15.17/7.63 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 15.17/7.63 % Starting SubtermCWHack with 136s (1) cores
% 15.17/7.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 15.17/7.63 % Starting E---G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 15.17/7.63 % Starting U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 15.17/7.63 % Preprocessing time : 0.001 s
% 15.17/7.63 % Presaturation interreduction done
% 15.17/7.63
% 15.17/7.63 % Proof found!
% 15.17/7.63 % SZS status Unsatisfiable
% 15.17/7.63 % SZS output start CNFRefutation
% See solution above
% 15.17/7.63 % Parsed axioms : 6
% 15.17/7.63 % Removed by relevancy pruning/SinE : 0
% 15.17/7.63 % Initial clauses : 6
% 15.17/7.63 % Removed in clause preprocessing : 0
% 15.17/7.63 % Initial clauses in saturation : 6
% 15.17/7.63 % Processed clauses : 1378
% 15.17/7.63 % ...of these trivial : 687
% 15.17/7.63 % ...subsumed : 271
% 15.17/7.63 % ...remaining for further processing : 420
% 15.17/7.63 % Other redundant clauses eliminated : 0
% 15.17/7.63 % Clauses deleted for lack of memory : 0
% 15.17/7.63 % Backward-subsumed : 1
% 15.17/7.63 % Backward-rewritten : 133
% 15.17/7.63 % Generated clauses : 91568
% 15.17/7.63 % ...of the previous two non-redundant : 77050
% 15.17/7.63 % ...aggressively subsumed : 0
% 15.17/7.63 % Contextual simplify-reflections : 0
% 15.17/7.63 % Paramodulations : 91568
% 15.17/7.63 % Factorizations : 0
% 15.17/7.63 % NegExts : 0
% 15.17/7.63 % Equation resolutions : 0
% 15.17/7.63 % Disequality decompositions : 0
% 15.17/7.63 % Total rewrite steps : 166936
% 15.17/7.63 % ...of those cached : 150487
% 15.17/7.63 % Propositional unsat checks : 0
% 15.17/7.63 % Propositional check models : 0
% 15.17/7.63 % Propositional check unsatisfiable : 0
% 15.17/7.63 % Propositional clauses : 0
% 15.17/7.63 % Propositional clauses after purity: 0
% 15.17/7.63 % Propositional unsat core size : 0
% 15.17/7.63 % Propositional preprocessing time : 0.000
% 15.17/7.63 % Propositional encoding time : 0.000
% 15.17/7.63 % Propositional solver time : 0.000
% 15.17/7.63 % Success case prop preproc time : 0.000
% 15.17/7.63 % Success case prop encoding time : 0.000
% 15.17/7.63 % Success case prop solver time : 0.000
% 15.17/7.63 % Current number of processed clauses : 280
% 15.17/7.63 % Positive orientable unit clauses : 271
% 15.17/7.63 % Positive unorientable unit clauses: 9
% 15.17/7.63 % Negative unit clauses : 0
% 15.17/7.63 % Non-unit-clauses : 0
% 15.17/7.63 % Current number of unprocessed clauses: 75062
% 15.17/7.63 % ...number of literals in the above : 75062
% 15.17/7.63 % Current number of archived formulas : 0
% 15.17/7.63 % Current number of archived clauses : 140
% 15.17/7.63 % Clause-clause subsumption calls (NU) : 0
% 15.17/7.63 % Rec. Clause-clause subsumption calls : 0
% 15.17/7.63 % Non-unit clause-clause subsumptions : 0
% 15.17/7.63 % Unit Clause-clause subsumption calls : 273
% 15.17/7.63 % Rewrite failures with RHS unbound : 0
% 15.17/7.63 % BW rewrite match attempts : 1928
% 15.17/7.63 % BW rewrite match successes : 165
% 15.17/7.63 % Condensation attempts : 0
% 15.17/7.63 % Condensation successes : 0
% 15.17/7.63 % Termbank termtop insertions : 2396600
% 15.17/7.63 % Search garbage collected termcells : 2
% 15.17/7.63
% 15.17/7.63 % -------------------------------------------------
% 15.17/7.63 % User time : 2.048 s
% 15.17/7.63 % System time : 0.092 s
% 15.17/7.63 % Total time : 2.140 s
% 15.17/7.63 % Maximum resident set size: 3632 pages
% 15.17/7.63
% 15.17/7.63 % -------------------------------------------------
% 15.17/7.63 % User time : 10.252 s
% 15.17/7.63 % System time : 0.457 s
% 15.17/7.63 % Total time : 10.709 s
% 15.17/7.63 % Maximum resident set size: 4864 pages
% 15.17/7.63 % E exiting
%------------------------------------------------------------------------------