%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG026-6 : 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 : 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 02:05:33 PM UTC 2026
% Result : Unsatisfiable 0.02s 0.46s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 10 RR)
% Number of literals : 44 ( 43 equ; 8 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 71 ( 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(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',additive_inverse_additive_inverse) ).
cnf(prove_teichmuller_identity,negated_conjecture,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_teichmuller_identity) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
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(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(right_multiplicative_zero,axiom,
multiply(X1,additive_identity) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_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(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(left_multiplicative_zero,axiom,
multiply(additive_identity,X1) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_multiplicative_zero) ).
cnf(c_0_12,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
associativity_for_addition ).
cnf(c_0_13,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
right_additive_inverse ).
cnf(c_0_14,axiom,
add(additive_identity,X1) = X1,
left_additive_identity ).
cnf(c_0_15,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_16,axiom,
additive_inverse(additive_inverse(X1)) = X1,
additive_inverse_additive_inverse ).
cnf(c_0_17,negated_conjecture,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
inference(fof_simplification,[status(thm)],[prove_teichmuller_identity]) ).
cnf(c_0_18,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_20,negated_conjecture,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
c_0_17 ).
cnf(c_0_21,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
associator ).
cnf(c_0_22,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),additive_inverse(add(add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d)))))),multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d)))) != additive_identity,
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_21]),c_0_21]),c_0_21]),c_0_21]),c_0_21]) ).
cnf(c_0_24,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_22]),c_0_19]) ).
cnf(c_0_25,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_26,negated_conjecture,
add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),add(multiply(multiply(a,b),multiply(c,d)),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(multiply(multiply(a,multiply(b,c)),d),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))),multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d))))))))) != additive_identity,
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)],[c_0_23,c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]) ).
cnf(c_0_27,plain,
add(multiply(X1,X2),additive_inverse(multiply(X1,add(X2,X3)))) = additive_inverse(multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,axiom,
multiply(X1,additive_identity) = additive_identity,
right_multiplicative_zero ).
cnf(c_0_29,plain,
additive_inverse(additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_30,axiom,
add(X1,additive_identity) = X1,
right_additive_identity ).
cnf(c_0_31,negated_conjecture,
add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(multiply(multiply(a,multiply(b,c)),d),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))),multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d))))))) != additive_identity,
inference(rw,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_32,plain,
add(additive_inverse(X1),additive_inverse(X2)) = additive_inverse(add(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_33,plain,
additive_inverse(multiply(X1,additive_inverse(X2))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_13]),c_0_28]),c_0_29]),c_0_30]) ).
cnf(c_0_34,negated_conjecture,
add(multiply(multiply(multiply(a,b),c),d),additive_inverse(add(multiply(a,multiply(b,multiply(c,d))),add(multiply(multiply(a,multiply(b,c)),d),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))),multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d))))))) != additive_identity,
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
additive_inverse(multiply(X1,X2)) = multiply(X1,additive_inverse(X2)),
inference(spm,[status(thm)],[c_0_16,c_0_33]) ).
cnf(c_0_36,plain,
add(multiply(X1,X2),add(multiply(X1,X3),X4)) = add(multiply(X1,add(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_12,c_0_25]) ).
cnf(c_0_37,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_38,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_39,negated_conjecture,
add(multiply(multiply(multiply(a,b),c),d),additive_inverse(add(multiply(a,multiply(b,multiply(c,d))),add(multiply(multiply(a,multiply(b,c)),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d)))))) != additive_identity,
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_36]),c_0_36]),c_0_19]),c_0_13]),c_0_28]),c_0_14]) ).
cnf(c_0_40,plain,
add(multiply(X1,X2),add(X3,multiply(X4,X2))) = add(X3,multiply(add(X4,X1),X2)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
add(multiply(X1,X2),multiply(add(X1,X3),additive_inverse(X2))) = multiply(X3,additive_inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_38]),c_0_35]),c_0_35]) ).
cnf(c_0_42,axiom,
multiply(additive_identity,X1) = additive_identity,
left_multiplicative_zero ).
cnf(c_0_43,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)],[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_12]),c_0_25]),c_0_25]),c_0_36]),c_0_25]),c_0_25]),c_0_13]),c_0_28]),c_0_28]),c_0_28]),c_0_14]),c_0_35]),c_0_41]),c_0_19]),c_0_13]),c_0_28]),c_0_28]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG026-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.37 % Computer : n002.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Mon Sep 21 04:14:32 UTC 2026
% 0.02/0.37 % CPUTime :
% 0.02/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.02/0.41 Running first-order theorem proving
% 0.02/0.41 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
% 0.02/0.46 % Version: 3.5.1
% 0.02/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.02/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.02/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.02/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.02/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.02/0.46 % Starting sh5l with 300s (1) cores
% 0.02/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2403567 completed with status 0
% 0.02/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.02/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.02/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.02/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.02/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.02/0.46 % No SInE strategy applied
% 0.02/0.46 % Search class: FUUPM-FFSF21-DFFFFFNN
% 0.02/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.02/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.02/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.02/0.46 % Starting G-E--_201_C45_F1_AE_CS_SP_PI_S0Y with 136s (1) cores
% 0.02/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.02/0.46 % Starting new_bool_1 with 136s (1) cores
% 0.02/0.46 % new_bool_3 with pid 2403576 completed with status 0
% 0.02/0.46 % Result found by new_bool_3
% 0.02/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.02/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.02/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.02/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.02/0.46 % No SInE strategy applied
% 0.02/0.46 % Search class: FUUPM-FFSF21-DFFFFFNN
% 0.02/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.02/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.02/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.02/0.46 % Starting G-E--_201_C45_F1_AE_CS_SP_PI_S0Y with 136s (1) cores
% 0.02/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.02/0.46 % Preprocessing time : 0.001 s
% 0.02/0.46 % Presaturation interreduction done
% 0.02/0.46
% 0.02/0.46 % Proof found!
% 0.02/0.46 % SZS status Unsatisfiable
% 0.02/0.46 % SZS output start CNFRefutation
% See solution above
% 0.02/0.46 % Parsed axioms : 16
% 0.02/0.46 % Removed by relevancy pruning/SinE : 0
% 0.02/0.46 % Initial clauses : 16
% 0.02/0.46 % Removed in clause preprocessing : 2
% 0.02/0.46 % Initial clauses in saturation : 14
% 0.02/0.46 % Processed clauses : 525
% 0.02/0.46 % ...of these trivial : 157
% 0.02/0.46 % ...subsumed : 275
% 0.02/0.46 % ...remaining for further processing : 92
% 0.02/0.46 % Other redundant clauses eliminated : 0
% 0.02/0.46 % Clauses deleted for lack of memory : 0
% 0.02/0.46 % Backward-subsumed : 0
% 0.02/0.46 % Backward-rewritten : 12
% 0.02/0.46 % Generated clauses : 3407
% 0.02/0.46 % ...of the previous two non-redundant : 2551
% 0.02/0.46 % ...aggressively subsumed : 0
% 0.02/0.46 % Contextual simplify-reflections : 0
% 0.02/0.46 % Paramodulations : 3407
% 0.02/0.46 % Factorizations : 0
% 0.02/0.46 % NegExts : 0
% 0.02/0.46 % Equation resolutions : 0
% 0.02/0.46 % Disequality decompositions : 0
% 0.02/0.46 % Total rewrite steps : 5668
% 0.02/0.46 % ...of those cached : 3862
% 0.02/0.46 % Propositional unsat checks : 0
% 0.02/0.46 % Propositional check models : 0
% 0.02/0.46 % Propositional check unsatisfiable : 0
% 0.02/0.46 % Propositional clauses : 0
% 0.02/0.46 % Propositional clauses after purity: 0
% 0.02/0.46 % Propositional unsat core size : 0
% 0.02/0.46 % Propositional preprocessing time : 0.000
% 0.02/0.46 % Propositional encoding time : 0.000
% 0.02/0.46 % Propositional solver time : 0.000
% 0.02/0.46 % Success case prop preproc time : 0.000
% 0.02/0.46 % Success case prop encoding time : 0.000
% 0.02/0.46 % Success case prop solver time : 0.000
% 0.02/0.46 % Current number of processed clauses : 67
% 0.02/0.46 % Positive orientable unit clauses : 60
% 0.02/0.46 % Positive unorientable unit clauses: 5
% 0.02/0.46 % Negative unit clauses : 2
% 0.02/0.46 % Non-unit-clauses : 0
% 0.02/0.46 % Current number of unprocessed clauses: 1970
% 0.02/0.46 % ...number of literals in the above : 1970
% 0.02/0.46 % Current number of archived formulas : 0
% 0.02/0.46 % Current number of archived clauses : 27
% 0.02/0.46 % Clause-clause subsumption calls (NU) : 0
% 0.02/0.46 % Rec. Clause-clause subsumption calls : 0
% 0.02/0.46 % Non-unit clause-clause subsumptions : 0
% 0.02/0.46 % Unit Clause-clause subsumption calls : 27
% 0.02/0.46 % Rewrite failures with RHS unbound : 0
% 0.02/0.46 % BW rewrite match attempts : 170
% 0.02/0.46 % BW rewrite match successes : 94
% 0.02/0.46 % Condensation attempts : 0
% 0.02/0.46 % Condensation successes : 0
% 0.02/0.46 % Termbank termtop insertions : 38435
% 0.02/0.46 % Search garbage collected termcells : 2
% 0.02/0.46
% 0.02/0.46 % -------------------------------------------------
% 0.02/0.46 % User time : 0.022 s
% 0.02/0.46 % System time : 0.006 s
% 0.02/0.46 % Total time : 0.028 s
% 0.02/0.46 % Maximum resident set size: 3592 pages
% 0.02/0.46
% 0.02/0.46 % -------------------------------------------------
% 0.02/0.46 % User time : 0.122 s
% 0.02/0.46 % System time : 0.029 s
% 0.02/0.46 % Total time : 0.151 s
% 0.02/0.46 % Maximum resident set size: 4608 pages
% 0.02/0.46 % E exiting
%------------------------------------------------------------------------------