%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP436-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:43:48 PM UTC 2026
% Result : Unsatisfiable 1.57s 0.68s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 4 RR)
% Number of literals : 44 ( 43 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 154 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),X1))))) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c_0_2,axiom,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),X1))))) = X4,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,X4))),inverse(X5))),multiply(X5,multiply(X3,X1))))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(X3,inverse(X4))),multiply(X4,multiply(X5,X1))))) = multiply(X6,multiply(multiply(inverse(X6),inverse(multiply(X3,X5))),inverse(X2))),
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(inverse(X1),inverse(multiply(X2,multiply(X3,inverse(multiply(multiply(X1,multiply(X4,inverse(X5))),multiply(X5,multiply(X2,X3)))))))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_4]) ).
cnf(c_0_6,plain,
multiply(inverse(X1),inverse(multiply(multiply(inverse(X2),inverse(multiply(X3,multiply(X1,multiply(X4,inverse(X2)))))),X3))) = X4,
inference(spm,[status(thm)],[c_0_5,c_0_2]) ).
cnf(c_0_7,plain,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(X4,X1))))) = multiply(inverse(X5),inverse(multiply(X2,multiply(X3,multiply(X4,inverse(X5)))))),
inference(spm,[status(thm)],[c_0_2,c_0_6]) ).
cnf(c_0_8,plain,
multiply(inverse(X1),inverse(multiply(multiply(X2,inverse(multiply(X3,multiply(X1,multiply(X4,X2))))),X3))) = X4,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(multiply(inverse(X2),inverse(multiply(X3,X4))),X3))),inverse(X2))) = X4,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_10,plain,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(X4,X1))))) = multiply(X5,inverse(multiply(X2,multiply(X3,multiply(X4,X5))))),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_11,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),inverse(X4))),multiply(X4,multiply(X5,X1))))) = inverse(multiply(multiply(X6,multiply(multiply(inverse(X6),inverse(multiply(X7,X3))),inverse(X8))),multiply(X8,multiply(X7,X5)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_12,plain,
multiply(inverse(X1),inverse(multiply(multiply(inverse(X2),inverse(multiply(X3,X4))),X3))) = multiply(inverse(X1),inverse(multiply(multiply(inverse(X2),inverse(multiply(X5,X4))),X5))),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
multiply(X1,multiply(X2,inverse(multiply(multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),inverse(X5))),multiply(X5,multiply(X1,X2)))))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_3]) ).
cnf(c_0_14,plain,
inverse(multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2)) = inverse(multiply(multiply(inverse(X1),inverse(multiply(X4,X3))),X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_12]),c_0_3]) ).
cnf(c_0_15,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),inverse(X4))) = multiply(X5,multiply(multiply(inverse(X5),inverse(multiply(X2,X3))),inverse(X4))),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_16,plain,
multiply(inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,X1))),multiply(inverse(X4),inverse(multiply(X5,X6))))))),inverse(multiply(X6,multiply(X4,X3)))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_17,plain,
multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2) = multiply(multiply(inverse(X1),inverse(multiply(X4,X3))),X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_13]) ).
cnf(c_0_18,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(X2)),inverse(X3))) = multiply(X4,multiply(multiply(inverse(X4),inverse(X2)),inverse(X3))),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),X4))))) = X1,
inference(spm,[status(thm)],[c_0_2,c_0_17]) ).
cnf(c_0_20,plain,
multiply(X1,multiply(inverse(X1),inverse(X2))) = multiply(X3,multiply(inverse(X3),inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_19]) ).
cnf(c_0_21,plain,
multiply(multiply(inverse(X1),inverse(X2)),X2) = multiply(multiply(inverse(X1),inverse(X3)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_19]) ).
cnf(c_0_22,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_19]),c_0_19]) ).
cnf(c_0_23,plain,
multiply(multiply(inverse(X1),inverse(X2)),X2) = multiply(multiply(X3,inverse(X3)),inverse(X1)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
multiply(X1,inverse(X1)) = multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),X4))),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_25,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,multiply(X3,inverse(multiply(X4,multiply(X5,multiply(X2,X3)))))))),inverse(X5))) = X4,
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_26,plain,
multiply(X1,inverse(X1)) = multiply(multiply(inverse(multiply(X2,inverse(X2))),inverse(X3)),X3),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
multiply(X1,inverse(multiply(inverse(X2),multiply(X3,multiply(inverse(X3),X1))))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_24]),c_0_19]) ).
cnf(c_0_28,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_24]),c_0_25]) ).
cnf(c_0_29,plain,
multiply(X1,inverse(X1)) = multiply(X2,multiply(inverse(X2),multiply(X3,inverse(X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_30,plain,
multiply(X1,inverse(multiply(inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),X5)))),multiply(X6,multiply(multiply(inverse(X6),inverse(X4)),X1))))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_31,plain,
multiply(X1,multiply(X2,inverse(X2))) = multiply(X3,multiply(inverse(X3),inverse(inverse(X1)))),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_32,plain,
multiply(X1,multiply(inverse(X1),inverse(inverse(X2)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_29]),c_0_28]),c_0_28]) ).
cnf(c_0_33,plain,
inverse(multiply(multiply(inverse(X1),inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),inverse(X1)))))),X2)) = inverse(X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_30]),c_0_2]) ).
cnf(c_0_34,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
inverse(multiply(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),X1))))),X2)) = inverse(X4),
inference(spm,[status(thm)],[c_0_33,c_0_10]) ).
cnf(c_0_36,plain,
multiply(multiply(inverse(X1),inverse(X2)),X2) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_34]),c_0_28]) ).
cnf(c_0_37,plain,
multiply(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),X1))))),X2) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_35]),c_0_13]) ).
cnf(c_0_38,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_36]),c_0_34]) ).
cnf(c_0_39,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(fof_simplification,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_0_40,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_34]),c_0_36]) ).
cnf(c_0_41,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
c_0_39 ).
cnf(c_0_42,plain,
multiply(X1,inverse(X1)) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_22,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP436-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:15:46 UTC 2026
% 0.04/0.37 % CPUTime :
% 0.04/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.41 Running first-order theorem proving
% 0.04/0.41 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
% 1.57/0.68 % Version: 3.5.1
% 1.57/0.68 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.57/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.57/0.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.57/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.57/0.68 % Starting new_bool_1 with 300s (1) cores
% 1.57/0.68 % Starting sh5l with 300s (1) cores
% 1.57/0.68 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1612531 completed with status 0
% 1.57/0.68 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 1.57/0.68 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.57/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.57/0.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.57/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.57/0.68 % No SInE strategy applied
% 1.57/0.68 % Search class: FUUPF-FFSF21-DFFFFFNN
% 1.57/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.57/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.57/0.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 1.57/0.68 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.57/0.68 % Starting new_bool_3 with 136s (1) cores
% 1.57/0.68 % Starting new_bool_1 with 136s (1) cores
% 1.57/0.68 % SubtermCWHack with pid 1612536 completed with status 0
% 1.57/0.68 % Result found by SubtermCWHack
% 1.57/0.68 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.57/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.57/0.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.57/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.57/0.68 % No SInE strategy applied
% 1.57/0.68 % Search class: FUUPF-FFSF21-DFFFFFNN
% 1.57/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.57/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.57/0.68 % Preprocessing time : 0.001 s
% 1.57/0.68
% 1.57/0.68 % Proof found!
% 1.57/0.68 % SZS status Unsatisfiable
% 1.57/0.68 % SZS output start CNFRefutation
% See solution above
% 1.57/0.68 % Parsed axioms : 2
% 1.57/0.68 % Removed by relevancy pruning/SinE : 0
% 1.57/0.68 % Initial clauses : 2
% 1.57/0.68 % Removed in clause preprocessing : 0
% 1.57/0.68 % Initial clauses in saturation : 2
% 1.57/0.68 % Processed clauses : 273
% 1.57/0.68 % ...of these trivial : 36
% 1.57/0.68 % ...subsumed : 159
% 1.57/0.68 % ...remaining for further processing : 78
% 1.57/0.68 % Other redundant clauses eliminated : 0
% 1.57/0.68 % Clauses deleted for lack of memory : 0
% 1.57/0.68 % Backward-subsumed : 4
% 1.57/0.68 % Backward-rewritten : 16
% 1.57/0.68 % Generated clauses : 19685
% 1.57/0.68 % ...of the previous two non-redundant : 18913
% 1.57/0.68 % ...aggressively subsumed : 0
% 1.57/0.68 % Contextual simplify-reflections : 0
% 1.57/0.68 % Paramodulations : 19685
% 1.57/0.68 % Factorizations : 0
% 1.57/0.68 % NegExts : 0
% 1.57/0.68 % Equation resolutions : 0
% 1.57/0.68 % Disequality decompositions : 0
% 1.57/0.68 % Total rewrite steps : 2497
% 1.57/0.68 % ...of those cached : 1334
% 1.57/0.68 % Propositional unsat checks : 0
% 1.57/0.68 % Propositional check models : 0
% 1.57/0.68 % Propositional check unsatisfiable : 0
% 1.57/0.68 % Propositional clauses : 0
% 1.57/0.68 % Propositional clauses after purity: 0
% 1.57/0.68 % Propositional unsat core size : 0
% 1.57/0.68 % Propositional preprocessing time : 0.000
% 1.57/0.68 % Propositional encoding time : 0.000
% 1.57/0.68 % Propositional solver time : 0.000
% 1.57/0.68 % Success case prop preproc time : 0.000
% 1.57/0.68 % Success case prop encoding time : 0.000
% 1.57/0.68 % Success case prop solver time : 0.000
% 1.57/0.68 % Current number of processed clauses : 58
% 1.57/0.68 % Positive orientable unit clauses : 42
% 1.57/0.68 % Positive unorientable unit clauses: 15
% 1.57/0.68 % Negative unit clauses : 1
% 1.57/0.68 % Non-unit-clauses : 0
% 1.57/0.68 % Current number of unprocessed clauses: 18414
% 1.57/0.68 % ...number of literals in the above : 18414
% 1.57/0.68 % Current number of archived formulas : 0
% 1.57/0.68 % Current number of archived clauses : 20
% 1.57/0.68 % Clause-clause subsumption calls (NU) : 0
% 1.57/0.68 % Rec. Clause-clause subsumption calls : 0
% 1.57/0.68 % Non-unit clause-clause subsumptions : 0
% 1.57/0.68 % Unit Clause-clause subsumption calls : 409
% 1.57/0.68 % Rewrite failures with RHS unbound : 1049
% 1.57/0.68 % BW rewrite match attempts : 1384
% 1.57/0.68 % BW rewrite match successes : 117
% 1.57/0.68 % Condensation attempts : 0
% 1.57/0.68 % Condensation successes : 0
% 1.57/0.68 % Termbank termtop insertions : 525142
% 1.57/0.68 % Search garbage collected termcells : 2
% 1.57/0.68
% 1.57/0.68 % -------------------------------------------------
% 1.57/0.68 % User time : 0.223 s
% 1.57/0.68 % System time : 0.022 s
% 1.57/0.68 % Total time : 0.245 s
% 1.57/0.68 % Maximum resident set size: 3636 pages
% 1.57/0.68
% 1.57/0.68 % -------------------------------------------------
% 1.57/0.68 % User time : 0.965 s
% 1.57/0.68 % System time : 0.082 s
% 1.57/0.68 % Total time : 1.048 s
% 1.57/0.68 % Maximum resident set size: 4864 pages
% 1.57/0.68 % E exiting
%------------------------------------------------------------------------------