%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG025-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 02:05:32 PM UTC 2026
% Result : Unsatisfiable 14.02s 2.51s
% Output : CNFRefutation 14.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 46 ( 46 unt; 0 nHn; 7 RR)
% Number of literals : 46 ( 45 equ; 6 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 85 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_for_addition,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
cnf(right_additive_inverse,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).
cnf(left_additive_identity,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).
cnf(distribute1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute1) ).
cnf(distribute2,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute2) ).
cnf(right_alternative,axiom,
multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_alternative) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
cnf(right_multiplicative_zero,axiom,
multiply(X1,additive_identity) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_multiplicative_zero) ).
cnf(left_alternative,axiom,
multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_alternative) ).
cnf(prove_flexible_law,negated_conjecture,
associator(x,y,x) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_flexible_law) ).
cnf(associator,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associator) ).
cnf(left_multiplicative_zero,axiom,
multiply(additive_identity,X1) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_multiplicative_zero) ).
cnf(right_additive_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
cnf(c_0_13,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
associativity_for_addition ).
cnf(c_0_14,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
right_additive_inverse ).
cnf(c_0_15,axiom,
add(additive_identity,X1) = X1,
left_additive_identity ).
cnf(c_0_16,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_17,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_18,axiom,
multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)),
right_alternative ).
cnf(c_0_19,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_20,axiom,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_21,plain,
add(multiply(X1,add(X2,X3)),X4) = add(multiply(X1,X2),add(multiply(X1,X3),X4)),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_22,axiom,
multiply(X1,additive_identity) = additive_identity,
right_multiplicative_zero ).
cnf(c_0_23,plain,
add(multiply(X1,X2),multiply(X3,multiply(X2,X2))) = multiply(add(X1,multiply(X3,X2)),X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,axiom,
multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
left_alternative ).
cnf(c_0_25,negated_conjecture,
associator(x,y,x) != additive_identity,
inference(fof_simplification,[status(thm)],[prove_flexible_law]) ).
cnf(c_0_26,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
add(multiply(X1,X2),add(multiply(X1,additive_inverse(X2)),X3)) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_14]),c_0_22]),c_0_15]) ).
cnf(c_0_28,plain,
add(multiply(X1,multiply(X1,X2)),multiply(X3,multiply(X2,X2))) = multiply(add(multiply(X1,X1),multiply(X3,X2)),X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
associator(x,y,x) != additive_identity,
c_0_25 ).
cnf(c_0_30,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
associator ).
cnf(c_0_31,plain,
add(multiply(add(X1,X2),X3),X4) = add(multiply(X1,X3),add(multiply(X2,X3),X4)),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_32,axiom,
multiply(additive_identity,X1) = additive_identity,
left_multiplicative_zero ).
cnf(c_0_33,plain,
additive_inverse(multiply(X1,X2)) = multiply(X1,additive_inverse(X2)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
multiply(multiply(X1,add(X1,X2)),X2) = multiply(X1,multiply(add(X1,X2),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_28]),c_0_16]),c_0_17]) ).
cnf(c_0_35,negated_conjecture,
add(multiply(multiply(x,y),x),additive_inverse(multiply(x,multiply(y,x)))) != additive_identity,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,plain,
add(multiply(X1,X2),add(multiply(additive_inverse(X1),X2),X3)) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_14]),c_0_32]),c_0_15]) ).
cnf(c_0_37,plain,
add(multiply(X1,multiply(X2,X2)),multiply(multiply(X1,X2),X3)) = multiply(multiply(X1,X2),add(X2,X3)),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_38,plain,
multiply(multiply(X1,add(X1,X2)),additive_inverse(X2)) = multiply(X1,multiply(add(X1,X2),additive_inverse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_33]),c_0_33]) ).
cnf(c_0_39,axiom,
add(X1,additive_identity) = X1,
right_additive_identity ).
cnf(c_0_40,negated_conjecture,
add(multiply(multiply(x,y),x),multiply(x,multiply(y,additive_inverse(x)))) != additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_33]),c_0_33]) ).
cnf(c_0_41,plain,
multiply(X1,additive_inverse(X2)) = multiply(additive_inverse(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_36]),c_0_33]) ).
cnf(c_0_42,plain,
multiply(multiply(X1,add(X1,X2)),X1) = multiply(X1,multiply(add(X1,X2),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_37,c_0_38]),c_0_16]),c_0_16]),c_0_13]),c_0_14]),c_0_39]),c_0_13]),c_0_14]),c_0_39]) ).
cnf(c_0_43,negated_conjecture,
add(multiply(multiply(x,y),x),multiply(x,multiply(additive_inverse(y),x))) != additive_identity,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,plain,
multiply(multiply(X1,X2),X1) = multiply(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_42,c_0_19]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[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)],[c_0_43,c_0_44]),c_0_16]),c_0_17]),c_0_14]),c_0_32]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG025-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:11:35 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 14.02/2.51 % Version: 3.5.1
% 14.02/2.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 14.02/2.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.02/2.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.02/2.51 % Starting new_bool_3 with 300s (1) cores
% 14.02/2.51 % Starting new_bool_1 with 300s (1) cores
% 14.02/2.51 % Starting sh5l with 300s (1) cores
% 14.02/2.51 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3108140 completed with status 0
% 14.02/2.51 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 14.02/2.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 14.02/2.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.02/2.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.02/2.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.02/2.51 % No SInE strategy applied
% 14.02/2.51 % Search class: FUUPM-FFSF21-MFFFFFNN
% 14.02/2.51 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 14.02/2.51 % Starting SubtermCWHack with 136s (1) cores
% 14.02/2.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.02/2.51 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 14.02/2.51 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 14.02/2.51 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 14.02/2.51 % H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with pid 3108146 completed with status 0
% 14.02/2.51 % Result found by H----_047_B31_F1_PI_AE_R4_CS_SP_S2S
% 14.02/2.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 14.02/2.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.02/2.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.02/2.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.02/2.51 % No SInE strategy applied
% 14.02/2.51 % Search class: FUUPM-FFSF21-MFFFFFNN
% 14.02/2.51 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 14.02/2.51 % Starting SubtermCWHack with 136s (1) cores
% 14.02/2.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.02/2.51 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 14.02/2.51 % Preprocessing time : 0.001 s
% 14.02/2.51
% 14.02/2.51 % Proof found!
% 14.02/2.51 % SZS status Unsatisfiable
% 14.02/2.51 % SZS output start CNFRefutation
% See solution above
% 14.02/2.51 % Parsed axioms : 16
% 14.02/2.51 % Removed by relevancy pruning/SinE : 0
% 14.02/2.51 % Initial clauses : 16
% 14.02/2.51 % Removed in clause preprocessing : 2
% 14.02/2.51 % Initial clauses in saturation : 14
% 14.02/2.51 % Processed clauses : 2162
% 14.02/2.51 % ...of these trivial : 781
% 14.02/2.51 % ...subsumed : 1082
% 14.02/2.51 % ...remaining for further processing : 299
% 14.02/2.51 % Other redundant clauses eliminated : 0
% 14.02/2.51 % Clauses deleted for lack of memory : 0
% 14.02/2.51 % Backward-subsumed : 3
% 14.02/2.51 % Backward-rewritten : 58
% 14.02/2.51 % Generated clauses : 57636
% 14.02/2.51 % ...of the previous two non-redundant : 50915
% 14.02/2.51 % ...aggressively subsumed : 0
% 14.02/2.51 % Contextual simplify-reflections : 0
% 14.02/2.51 % Paramodulations : 57636
% 14.02/2.51 % Factorizations : 0
% 14.02/2.51 % NegExts : 0
% 14.02/2.51 % Equation resolutions : 0
% 14.02/2.51 % Disequality decompositions : 0
% 14.02/2.51 % Total rewrite steps : 218425
% 14.02/2.51 % ...of those cached : 198041
% 14.02/2.51 % Propositional unsat checks : 0
% 14.02/2.51 % Propositional check models : 0
% 14.02/2.51 % Propositional check unsatisfiable : 0
% 14.02/2.51 % Propositional clauses : 0
% 14.02/2.51 % Propositional clauses after purity: 0
% 14.02/2.51 % Propositional unsat core size : 0
% 14.02/2.51 % Propositional preprocessing time : 0.000
% 14.02/2.51 % Propositional encoding time : 0.000
% 14.02/2.51 % Propositional solver time : 0.000
% 14.02/2.51 % Success case prop preproc time : 0.000
% 14.02/2.51 % Success case prop encoding time : 0.000
% 14.02/2.51 % Success case prop solver time : 0.000
% 14.02/2.51 % Current number of processed clauses : 238
% 14.02/2.51 % Positive orientable unit clauses : 198
% 14.02/2.51 % Positive unorientable unit clauses: 40
% 14.02/2.51 % Negative unit clauses : 0
% 14.02/2.51 % Non-unit-clauses : 0
% 14.02/2.51 % Current number of unprocessed clauses: 48519
% 14.02/2.51 % ...number of literals in the above : 48519
% 14.02/2.51 % Current number of archived formulas : 0
% 14.02/2.51 % Current number of archived clauses : 63
% 14.02/2.51 % Clause-clause subsumption calls (NU) : 0
% 14.02/2.51 % Rec. Clause-clause subsumption calls : 0
% 14.02/2.51 % Non-unit clause-clause subsumptions : 0
% 14.02/2.51 % Unit Clause-clause subsumption calls : 705
% 14.02/2.51 % Rewrite failures with RHS unbound : 0
% 14.02/2.51 % BW rewrite match attempts : 1927
% 14.02/2.51 % BW rewrite match successes : 360
% 14.02/2.51 % Condensation attempts : 0
% 14.02/2.51 % Condensation successes : 0
% 14.02/2.51 % Termbank termtop insertions : 1381237
% 14.02/2.51 % Search garbage collected termcells : 2
% 14.02/2.51
% 14.02/2.51 % -------------------------------------------------
% 14.02/2.51 % User time : 1.898 s
% 14.02/2.51 % System time : 0.094 s
% 14.02/2.51 % Total time : 1.992 s
% 14.02/2.51 % Maximum resident set size: 3644 pages
% 14.02/2.51
% 14.02/2.51 % -------------------------------------------------
% 14.02/2.51 % User time : 9.345 s
% 14.02/2.51 % System time : 0.484 s
% 14.02/2.51 % Total time : 9.828 s
% 14.02/2.51 % Maximum resident set size: 4608 pages
% 14.02/2.51 % E exiting
%------------------------------------------------------------------------------