%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP731-1 : TPTP v9.3.1. Released v4.0.0.
% 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 12:41:03 PM UTC 2026
% Result : Unsatisfiable 2.09s 0.70s
% Output : CNFRefutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of clauses : 51 ( 51 unt; 0 nHn; 5 RR)
% Number of literals : 51 ( 50 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 : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 104 ( 25 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c06,axiom,
mult(i(X1),mult(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
cnf(c04,axiom,
mult(i(X1),X1) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
cnf(c02,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
cnf(c05,axiom,
i(mult(X1,X2)) = mult(i(X1),i(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
cnf(c10,axiom,
mult(mult(X1,X2),X3) = mult(mult(X1,mult(X2,X3)),asoc(X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10) ).
cnf(c11,axiom,
mult(X1,X2) = mult(mult(X2,X1),op_k(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c11) ).
cnf(c01,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
cnf(c03,axiom,
mult(X1,i(X1)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
cnf(c21,axiom,
asoc(asoc(X1,X2,X3),X4,X5) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c21) ).
cnf(c07,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
cnf(c09,axiom,
mult(mult(X1,mult(X2,X1)),X3) = mult(X1,mult(X2,mult(X1,X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
cnf(c08,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
cnf(goals,negated_conjecture,
op_k(asoc(a,b,c),d) != unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_13,axiom,
mult(i(X1),mult(X1,X2)) = X2,
c06 ).
cnf(c_0_14,axiom,
mult(i(X1),X1) = unit,
c04 ).
cnf(c_0_15,axiom,
mult(X1,unit) = X1,
c02 ).
cnf(c_0_16,axiom,
i(mult(X1,X2)) = mult(i(X1),i(X2)),
c05 ).
cnf(c_0_17,plain,
i(i(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,axiom,
mult(mult(X1,X2),X3) = mult(mult(X1,mult(X2,X3)),asoc(X1,X2,X3)),
c10 ).
cnf(c_0_19,plain,
mult(X1,i(mult(X1,X2))) = i(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_16]),c_0_17]) ).
cnf(c_0_20,axiom,
mult(X1,X2) = mult(mult(X2,X1),op_k(X1,X2)),
c11 ).
cnf(c_0_21,axiom,
mult(unit,X1) = X1,
c01 ).
cnf(c_0_22,axiom,
mult(X1,i(X1)) = unit,
c03 ).
cnf(c_0_23,plain,
mult(i(mult(X1,mult(X2,X3))),mult(mult(X1,X2),X3)) = asoc(X1,X2,X3),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_24,plain,
mult(mult(X1,X2),i(mult(X2,X1))) = i(op_k(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
i(unit) = unit,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
asoc(asoc(X1,X2,X3),X4,X5) = unit,
c21 ).
cnf(c_0_27,plain,
asoc(X1,X2,i(mult(X2,X1))) = i(op_k(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_19]),c_0_22]),c_0_25]),c_0_21]) ).
cnf(c_0_28,axiom,
rd(mult(X1,X2),X2) = X1,
c07 ).
cnf(c_0_29,axiom,
mult(mult(X1,mult(X2,X1)),X3) = mult(X1,mult(X2,mult(X1,X3))),
c09 ).
cnf(c_0_30,plain,
i(op_k(X1,asoc(X2,X3,X4))) = unit,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
rd(mult(X1,mult(X2,mult(X1,X3))),X3) = mult(X1,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
rd(X1,mult(X2,X1)) = i(X2),
inference(spm,[status(thm)],[c_0_28,c_0_13]) ).
cnf(c_0_33,axiom,
mult(rd(X1,X2),X2) = X1,
c08 ).
cnf(c_0_34,plain,
mult(X1,mult(i(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_35,plain,
op_k(X1,asoc(X2,X3,X4)) = unit,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_30]),c_0_15]) ).
cnf(c_0_36,plain,
mult(X1,mult(i(mult(X1,X2)),X1)) = rd(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_14]),c_0_15]) ).
cnf(c_0_37,plain,
i(rd(X1,X2)) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
i(mult(i(X1),X2)) = mult(X1,i(X2)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_39,plain,
mult(X1,op_k(mult(i(X2),X1),X2)) = mult(mult(i(X2),X1),X2),
inference(spm,[status(thm)],[c_0_20,c_0_34]) ).
cnf(c_0_40,plain,
op_k(X1,i(op_k(X2,X3))) = unit,
inference(spm,[status(thm)],[c_0_35,c_0_27]) ).
cnf(c_0_41,plain,
mult(mult(X1,X2),i(X1)) = mult(X1,rd(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_36]),c_0_37]),c_0_38]) ).
cnf(c_0_42,plain,
mult(op_k(X1,X2),rd(X3,op_k(X1,X2))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_15]),c_0_17]),c_0_41]) ).
cnf(c_0_43,plain,
rd(X1,rd(X1,op_k(X2,X3))) = op_k(X2,X3),
inference(spm,[status(thm)],[c_0_28,c_0_42]) ).
cnf(c_0_44,plain,
rd(mult(X1,X2),op_k(X1,X2)) = mult(X2,X1),
inference(spm,[status(thm)],[c_0_28,c_0_20]) ).
cnf(c_0_45,plain,
rd(mult(X1,X2),mult(X2,X1)) = op_k(X1,X2),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_46,negated_conjecture,
op_k(asoc(a,b,c),d) != unit,
inference(fof_simplification,[status(thm)],[goals]) ).
cnf(c_0_47,plain,
i(op_k(X1,X2)) = op_k(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_45]),c_0_45]) ).
cnf(c_0_48,negated_conjecture,
op_k(asoc(a,b,c),d) != unit,
c_0_46 ).
cnf(c_0_49,plain,
op_k(asoc(X1,X2,X3),X4) = unit,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_35]),c_0_25]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP731-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n010.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 20 20:36:09 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 2.09/0.70 % Version: 3.5.1
% 2.09/0.70 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.09/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.09/0.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.09/0.70 % Starting new_bool_3 with 300s (1) cores
% 2.09/0.70 % Starting new_bool_1 with 300s (1) cores
% 2.09/0.70 % Starting sh5l with 300s (1) cores
% 2.09/0.70 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3477117 completed with status 0
% 2.09/0.70 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.09/0.70 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.09/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.09/0.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.09/0.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.09/0.70 % No SInE strategy applied
% 2.09/0.70 % Search class: FUUPM-FFMF32-DFFFFFNN
% 2.09/0.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.09/0.70 % Starting SubtermCWHack with 136s (1) cores
% 2.09/0.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.09/0.70 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 226s (1) cores
% 2.09/0.70 % Starting new_bool_3 with 226s (1) cores
% 2.09/0.70 % Starting new_bool_1 with 226s (1) cores
% 2.09/0.70 % SubtermCWHack with pid 3477124 completed with status 0
% 2.09/0.70 % Result found by SubtermCWHack
% 2.09/0.70 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.09/0.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.09/0.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.09/0.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.09/0.70 % No SInE strategy applied
% 2.09/0.70 % Search class: FUUPM-FFMF32-DFFFFFNN
% 2.09/0.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.09/0.70 % Starting SubtermCWHack with 136s (1) cores
% 2.09/0.70 % Preprocessing time : 0.001 s
% 2.09/0.70
% 2.09/0.70 % Proof found!
% 2.09/0.70 % SZS status Unsatisfiable
% 2.09/0.70 % SZS output start CNFRefutation
% See solution above
% 2.09/0.70 % Parsed axioms : 23
% 2.09/0.70 % Removed by relevancy pruning/SinE : 0
% 2.09/0.70 % Initial clauses : 23
% 2.09/0.70 % Removed in clause preprocessing : 3
% 2.09/0.70 % Initial clauses in saturation : 20
% 2.09/0.70 % Processed clauses : 541
% 2.09/0.70 % ...of these trivial : 247
% 2.09/0.70 % ...subsumed : 79
% 2.09/0.70 % ...remaining for further processing : 215
% 2.09/0.70 % Other redundant clauses eliminated : 0
% 2.09/0.70 % Clauses deleted for lack of memory : 0
% 2.09/0.70 % Backward-subsumed : 0
% 2.09/0.70 % Backward-rewritten : 55
% 2.09/0.70 % Generated clauses : 18089
% 2.09/0.70 % ...of the previous two non-redundant : 12761
% 2.09/0.70 % ...aggressively subsumed : 0
% 2.09/0.70 % Contextual simplify-reflections : 0
% 2.09/0.70 % Paramodulations : 18089
% 2.09/0.70 % Factorizations : 0
% 2.09/0.70 % NegExts : 0
% 2.09/0.70 % Equation resolutions : 0
% 2.09/0.70 % Disequality decompositions : 0
% 2.09/0.70 % Total rewrite steps : 28322
% 2.09/0.70 % ...of those cached : 23958
% 2.09/0.70 % Propositional unsat checks : 0
% 2.09/0.70 % Propositional check models : 0
% 2.09/0.70 % Propositional check unsatisfiable : 0
% 2.09/0.70 % Propositional clauses : 0
% 2.09/0.70 % Propositional clauses after purity: 0
% 2.09/0.70 % Propositional unsat core size : 0
% 2.09/0.70 % Propositional preprocessing time : 0.000
% 2.09/0.70 % Propositional encoding time : 0.000
% 2.09/0.70 % Propositional solver time : 0.000
% 2.09/0.70 % Success case prop preproc time : 0.000
% 2.09/0.70 % Success case prop encoding time : 0.000
% 2.09/0.70 % Success case prop solver time : 0.000
% 2.09/0.70 % Current number of processed clauses : 160
% 2.09/0.70 % Positive orientable unit clauses : 153
% 2.09/0.70 % Positive unorientable unit clauses: 7
% 2.09/0.70 % Negative unit clauses : 0
% 2.09/0.70 % Non-unit-clauses : 0
% 2.09/0.70 % Current number of unprocessed clauses: 12059
% 2.09/0.70 % ...number of literals in the above : 12059
% 2.09/0.70 % Current number of archived formulas : 0
% 2.09/0.70 % Current number of archived clauses : 58
% 2.09/0.70 % Clause-clause subsumption calls (NU) : 0
% 2.09/0.70 % Rec. Clause-clause subsumption calls : 0
% 2.09/0.70 % Non-unit clause-clause subsumptions : 0
% 2.09/0.70 % Unit Clause-clause subsumption calls : 6
% 2.09/0.70 % Rewrite failures with RHS unbound : 0
% 2.09/0.70 % BW rewrite match attempts : 428
% 2.09/0.70 % BW rewrite match successes : 74
% 2.09/0.70 % Condensation attempts : 0
% 2.09/0.70 % Condensation successes : 0
% 2.09/0.70 % Termbank termtop insertions : 296005
% 2.09/0.70 % Search garbage collected termcells : 2
% 2.09/0.70
% 2.09/0.70 % -------------------------------------------------
% 2.09/0.70 % User time : 0.227 s
% 2.09/0.70 % System time : 0.024 s
% 2.09/0.70 % Total time : 0.252 s
% 2.09/0.70 % Maximum resident set size: 3644 pages
% 2.09/0.70
% 2.09/0.70 % -------------------------------------------------
% 2.09/0.70 % User time : 1.063 s
% 2.09/0.70 % System time : 0.099 s
% 2.09/0.70 % Total time : 1.162 s
% 2.09/0.70 % Maximum resident set size: 4864 pages
% 2.09/0.70 % E exiting
%------------------------------------------------------------------------------