%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG029-3 : TPTP v9.3.1. Bugfixed v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 02:05:34 PM UTC 2026
% Result : Unsatisfiable 204.28s 30.67s
% Output : CNFRefutation 204.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 45 ( 40 unt; 0 nHn; 9 RR)
% Number of literals : 50 ( 49 equ; 8 neg)
% Maximal clause size : 2 ( 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; 3 con; 0-3 aty)
% Number of variables : 112 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associator_skew_symmetry2,axiom,
associator(X1,X2,X3) = additive_inverse(associator(X3,X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator_skew_symmetry2) ).
cnf(associator,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator) ).
cnf(associator_skew_symmetry1,axiom,
associator(X1,X2,X3) = additive_inverse(associator(X2,X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator_skew_symmetry1) ).
cnf(inverse_product2,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',inverse_product2) ).
cnf(inverse_product1,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',inverse_product1) ).
cnf(left_cancellation_for_addition,axiom,
( add(X1,X2) != add(X3,X2)
| X1 = X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',left_cancellation_for_addition) ).
cnf(sum_of_inverses,axiom,
additive_inverse(add(X1,X2)) = add(additive_inverse(X1),additive_inverse(X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',sum_of_inverses) ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',additive_inverse_additive_inverse) ).
cnf(multiply_over_add1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',multiply_over_add1) ).
cnf(right_moufang,hypothesis,
multiply(X1,multiply(X2,multiply(X3,X2))) = multiply(multiply(multiply(X1,X2),X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_moufang) ).
cnf(left_moufang,hypothesis,
multiply(multiply(X1,multiply(X2,X1)),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_moufang) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',commutativity_for_addition) ).
cnf(prove_middle_law,negated_conjecture,
multiply(multiply(cx,cy),multiply(cz,cx)) != multiply(cx,multiply(multiply(cy,cz),cx)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_middle_law) ).
cnf(c_0_13,axiom,
associator(X1,X2,X3) = additive_inverse(associator(X3,X2,X1)),
associator_skew_symmetry2 ).
cnf(c_0_14,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
associator ).
cnf(c_0_15,axiom,
associator(X1,X2,X3) = additive_inverse(associator(X2,X1,X3)),
associator_skew_symmetry1 ).
cnf(c_0_16,plain,
add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))) = additive_inverse(add(multiply(multiply(X3,X2),X1),additive_inverse(multiply(X3,multiply(X2,X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
cnf(c_0_17,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
inverse_product2 ).
cnf(c_0_18,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
inverse_product1 ).
cnf(c_0_19,plain,
( add(X1,X2) != add(X3,X2)
| X1 = X3 ),
inference(fof_simplification,[status(thm)],[left_cancellation_for_addition]) ).
cnf(c_0_20,plain,
add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))) = additive_inverse(add(multiply(multiply(X2,X1),X3),additive_inverse(multiply(X2,multiply(X1,X3))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_14]),c_0_14]) ).
cnf(c_0_21,plain,
additive_inverse(add(multiply(multiply(X1,X2),X3),multiply(X1,multiply(X2,additive_inverse(X3))))) = add(multiply(multiply(X3,X2),X1),multiply(X3,multiply(X2,additive_inverse(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]),c_0_17]),c_0_17]) ).
cnf(c_0_22,plain,
multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
inference(rw,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_23,axiom,
additive_inverse(add(X1,X2)) = add(additive_inverse(X1),additive_inverse(X2)),
sum_of_inverses ).
cnf(c_0_24,axiom,
additive_inverse(additive_inverse(X1)) = X1,
additive_inverse_additive_inverse ).
cnf(c_0_25,plain,
( add(X1,X2) != add(X3,X2)
| X1 = X3 ),
c_0_19 ).
cnf(c_0_26,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
multiply_over_add1 ).
cnf(c_0_27,hypothesis,
multiply(X1,multiply(X2,multiply(X3,X2))) = multiply(multiply(multiply(X1,X2),X3),X2),
right_moufang ).
cnf(c_0_28,plain,
add(multiply(multiply(X1,X2),X3),multiply(X1,multiply(X2,additive_inverse(X3)))) = add(multiply(multiply(X2,X3),X1),multiply(X2,multiply(X3,additive_inverse(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_17]),c_0_17]),c_0_21]),c_0_17]),c_0_17]) ).
cnf(c_0_29,hypothesis,
multiply(multiply(X1,multiply(X2,X1)),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
left_moufang ).
cnf(c_0_30,axiom,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_31,plain,
multiply(multiply(X1,additive_inverse(X2)),X3) = multiply(multiply(X1,X2),additive_inverse(X3)),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_32,plain,
additive_inverse(add(X1,additive_inverse(X2))) = add(additive_inverse(X1),X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_33,plain,
( add(X1,multiply(X2,X4)) != multiply(X2,add(X3,X4))
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,hypothesis,
additive_inverse(add(multiply(X1,multiply(X2,multiply(X3,X2))),multiply(multiply(X1,X2),multiply(X3,additive_inverse(X2))))) = add(multiply(multiply(X2,X3),multiply(X1,X2)),multiply(X2,multiply(X3,multiply(X1,additive_inverse(X2))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_27]),c_0_17]) ).
cnf(c_0_35,hypothesis,
add(multiply(X1,multiply(X2,multiply(X3,X2))),multiply(multiply(X1,X2),multiply(X3,additive_inverse(X2)))) = multiply(X2,add(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),additive_inverse(X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_27]),c_0_29]),c_0_26]) ).
cnf(c_0_36,plain,
additive_inverse(add(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),additive_inverse(X3)))) = add(multiply(X3,multiply(X2,X1)),multiply(multiply(X3,X2),additive_inverse(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_21,c_0_24]),c_0_22]),c_0_22]),c_0_17]),c_0_24]),c_0_30]),c_0_31]),c_0_30]) ).
cnf(c_0_37,plain,
additive_inverse(add(X1,multiply(X2,additive_inverse(X3)))) = add(additive_inverse(X1),multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_32,c_0_17]) ).
cnf(c_0_38,negated_conjecture,
multiply(multiply(cx,cy),multiply(cz,cx)) != multiply(cx,multiply(multiply(cy,cz),cx)),
inference(fof_simplification,[status(thm)],[prove_middle_law]) ).
cnf(c_0_39,plain,
( add(X1,multiply(X2,multiply(X3,multiply(X4,additive_inverse(X5))))) != multiply(X2,add(multiply(multiply(X4,X5),X3),multiply(X4,multiply(X5,additive_inverse(X3)))))
| X1 = multiply(X2,multiply(multiply(X3,X4),X5)) ),
inference(spm,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_40,hypothesis,
add(multiply(multiply(X1,X2),multiply(X3,X1)),multiply(X1,multiply(X2,multiply(X3,additive_inverse(X1))))) = multiply(X1,add(multiply(X2,multiply(X1,X3)),multiply(multiply(X2,X1),additive_inverse(X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_17]),c_0_36]) ).
cnf(c_0_41,plain,
add(multiply(multiply(X1,X2),X3),multiply(X1,multiply(X2,additive_inverse(X3)))) = add(multiply(X3,multiply(X2,X1)),multiply(multiply(X3,X2),additive_inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_17]),c_0_17]),c_0_30]) ).
cnf(c_0_42,negated_conjecture,
multiply(multiply(cx,cy),multiply(cz,cx)) != multiply(cx,multiply(multiply(cy,cz),cx)),
c_0_38 ).
cnf(c_0_43,hypothesis,
multiply(multiply(X1,X2),multiply(X3,X1)) = multiply(X1,multiply(multiply(X2,X3),X1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG029-3 : TPTP v9.3.1. Bugfixed v2.4.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 % Computer : n014.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Mon Sep 21 04:13:07 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.49 Running first-order theorem proving
% 0.20/0.49 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 204.28/30.67 % Version: 3.5.1
% 204.28/30.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 204.28/30.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 204.28/30.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 204.28/30.67 % Starting new_bool_3 with 300s (1) cores
% 204.28/30.67 % Starting new_bool_1 with 300s (1) cores
% 204.28/30.67 % Starting sh5l with 300s (1) cores
% 204.28/30.67 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3110213 completed with status 0
% 204.28/30.67 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 204.28/30.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 204.28/30.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 204.28/30.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 204.28/30.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 204.28/30.67 % No SInE strategy applied
% 204.28/30.67 % Search class: FHUPM-FFMF21-MFFFFFNN
% 204.28/30.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 204.28/30.67 % Starting SubtermCWHack with 136s (1) cores
% 204.28/30.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 204.28/30.67 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 204.28/30.67 % Starting new_bool_3 with 136s (1) cores
% 204.28/30.67 % Starting new_bool_1 with 136s (1) cores
% 204.28/30.67 % new_bool_3 with pid 3110222 completed with status 0
% 204.28/30.67 % Result found by new_bool_3
% 204.28/30.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 204.28/30.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 204.28/30.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 204.28/30.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 204.28/30.67 % No SInE strategy applied
% 204.28/30.67 % Search class: FHUPM-FFMF21-MFFFFFNN
% 204.28/30.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 204.28/30.67 % Starting SubtermCWHack with 136s (1) cores
% 204.28/30.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 204.28/30.67 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 204.28/30.67 % Starting new_bool_3 with 136s (1) cores
% 204.28/30.67 % Preprocessing time : 0.002 s
% 204.28/30.67 % Presaturation interreduction done
% 204.28/30.67
% 204.28/30.67 % Proof found!
% 204.28/30.67 % SZS status Unsatisfiable
% 204.28/30.67 % SZS output start CNFRefutation
% See solution above
% 204.28/30.67 % Parsed axioms : 24
% 204.28/30.67 % Removed by relevancy pruning/SinE : 0
% 204.28/30.67 % Initial clauses : 24
% 204.28/30.67 % Removed in clause preprocessing : 1
% 204.28/30.67 % Initial clauses in saturation : 23
% 204.28/30.67 % Processed clauses : 16581
% 204.28/30.67 % ...of these trivial : 350
% 204.28/30.67 % ...subsumed : 14443
% 204.28/30.67 % ...remaining for further processing : 1788
% 204.28/30.67 % Other redundant clauses eliminated : 4915
% 204.28/30.67 % Clauses deleted for lack of memory : 0
% 204.28/30.67 % Backward-subsumed : 50
% 204.28/30.67 % Backward-rewritten : 152
% 204.28/30.67 % Generated clauses : 587204
% 204.28/30.67 % ...of the previous two non-redundant : 556676
% 204.28/30.67 % ...aggressively subsumed : 0
% 204.28/30.67 % Contextual simplify-reflections : 0
% 204.28/30.67 % Paramodulations : 582179
% 204.28/30.67 % Factorizations : 0
% 204.28/30.67 % NegExts : 0
% 204.28/30.67 % Equation resolutions : 5025
% 204.28/30.67 % Disequality decompositions : 0
% 204.28/30.67 % Total rewrite steps : 2304233
% 204.28/30.67 % ...of those cached : 2187397
% 204.28/30.67 % Propositional unsat checks : 0
% 204.28/30.67 % Propositional check models : 0
% 204.28/30.67 % Propositional check unsatisfiable : 0
% 204.28/30.67 % Propositional clauses : 0
% 204.28/30.67 % Propositional clauses after purity: 0
% 204.28/30.67 % Propositional unsat core size : 0
% 204.28/30.67 % Propositional preprocessing time : 0.000
% 204.28/30.67 % Propositional encoding time : 0.000
% 204.28/30.67 % Propositional solver time : 0.000
% 204.28/30.67 % Success case prop preproc time : 0.000
% 204.28/30.67 % Success case prop encoding time : 0.000
% 204.28/30.67 % Success case prop solver time : 0.000
% 204.28/30.67 % Current number of processed clauses : 1563
% 204.28/30.67 % Positive orientable unit clauses : 310
% 204.28/30.67 % Positive unorientable unit clauses: 39
% 204.28/30.67 % Negative unit clauses : 0
% 204.28/30.67 % Non-unit-clauses : 1214
% 204.28/30.67 % Current number of unprocessed clauses: 539522
% 204.28/30.67 % ...number of literals in the above : 916509
% 204.28/30.67 % Current number of archived formulas : 0
% 204.28/30.67 % Current number of archived clauses : 226
% 204.28/30.67 % Clause-clause subsumption calls (NU) : 632976
% 204.28/30.67 % Rec. Clause-clause subsumption calls : 590013
% 204.28/30.67 % Non-unit clause-clause subsumptions : 13986
% 204.28/30.67 % Unit Clause-clause subsumption calls : 980
% 204.28/30.67 % Rewrite failures with RHS unbound : 0
% 204.28/30.67 % BW rewrite match attempts : 8761
% 204.28/30.67 % BW rewrite match successes : 750
% 204.28/30.67 % Condensation attempts : 0
% 204.28/30.67 % Condensation successes : 0
% 204.28/30.67 % Termbank termtop insertions : 16751239
% 204.28/30.67 % Search garbage collected termcells : 8
% 204.28/30.67
% 204.28/30.67 % -------------------------------------------------
% 204.28/30.67 % User time : 28.324 s
% 204.28/30.67 % System time : 0.899 s
% 204.28/30.67 % Total time : 29.223 s
% 204.28/30.67 % Maximum resident set size: 3392 pages
% 204.28/30.67
% 204.28/30.67 % -------------------------------------------------
% 204.28/30.67 % User time : 139.752 s
% 204.28/30.67 % System time : 4.488 s
% 204.28/30.67 % Total time : 144.240 s
% 204.28/30.67 % Maximum resident set size: 4608 pages
% 204.28/30.67 % E exiting
%------------------------------------------------------------------------------