%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG019-7 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 02:05:31 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 8 RR)
% Number of literals : 26 ( 25 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 48 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_linearised_form1,negated_conjecture,
associator(x,y,add(u,v)) != add(associator(x,y,u),associator(x,y,v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_linearised_form1) ).
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/Axioms/RNG003-0.ax',associator) ).
cnf(inverse_product2,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product2) ).
cnf(associativity_for_addition,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
cnf(inverse_product1,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product1) ).
cnf(distribute1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',distribute1) ).
cnf(distributivity_of_difference3,axiom,
multiply(additive_inverse(X1),add(X2,X3)) = add(additive_inverse(multiply(X1,X2)),additive_inverse(multiply(X1,X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_of_difference3) ).
cnf(c_0_8,negated_conjecture,
associator(x,y,add(u,v)) != add(associator(x,y,u),associator(x,y,v)),
inference(fof_simplification,[status(thm)],[prove_linearised_form1]) ).
cnf(c_0_9,negated_conjecture,
associator(x,y,add(u,v)) != add(associator(x,y,u),associator(x,y,v)),
c_0_8 ).
cnf(c_0_10,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
associator ).
cnf(c_0_11,negated_conjecture,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]),c_0_10]) ).
cnf(c_0_12,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
inverse_product2 ).
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,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_15,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
inverse_product1 ).
cnf(c_0_16,negated_conjecture,
add(multiply(multiply(x,y),u),add(multiply(x,multiply(y,additive_inverse(u))),add(multiply(multiply(x,y),v),multiply(x,multiply(y,additive_inverse(v)))))) != add(multiply(multiply(x,y),add(u,v)),multiply(x,multiply(y,additive_inverse(add(u,v))))),
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_11,c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_13]) ).
cnf(c_0_17,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_18,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_19,axiom,
multiply(additive_inverse(X1),add(X2,X3)) = add(additive_inverse(multiply(X1,X2)),additive_inverse(multiply(X1,X3))),
distributivity_of_difference3 ).
cnf(c_0_20,plain,
multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
inference(rw,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_21,negated_conjecture,
add(multiply(multiply(x,y),u),add(multiply(multiply(x,y),v),multiply(x,multiply(y,add(additive_inverse(u),additive_inverse(v)))))) != add(multiply(multiply(x,y),add(u,v)),multiply(x,multiply(y,additive_inverse(add(u,v))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_18]),c_0_14]) ).
cnf(c_0_22,plain,
multiply(X1,add(additive_inverse(X2),additive_inverse(X3))) = multiply(X1,additive_inverse(add(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_12]),c_0_12]),c_0_18]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
add(multiply(multiply(x,y),u),add(multiply(multiply(x,y),v),multiply(x,multiply(y,additive_inverse(add(u,v)))))) != add(multiply(multiply(x,y),add(u,v)),multiply(x,multiply(y,additive_inverse(add(u,v))))),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
add(multiply(X1,X2),add(multiply(X1,X3),X4)) = add(multiply(X1,add(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG019-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:11:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.43 % Version: 3.5.1
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % Starting sh5l with 300s (1) cores
% 0.10/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 945515 completed with status 0
% 0.10/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.43 % No SInE strategy applied
% 0.10/0.43 % Search class: FUUPM-FFMF21-MFFFFFNN
% 0.10/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.43 % Starting U----_210g_10_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.10/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.10/0.43 % U----_210g_10_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 945522 completed with status 0
% 0.10/0.43 % Result found by U----_210g_10_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.43 % No SInE strategy applied
% 0.10/0.43 % Search class: FUUPM-FFMF21-MFFFFFNN
% 0.10/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.43 % Starting U----_210g_10_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.10/0.43 % Preprocessing time : 0.001 s
% 0.10/0.43 % Presaturation interreduction done
% 0.10/0.43
% 0.10/0.43 % Proof found!
% 0.10/0.43 % SZS status Unsatisfiable
% 0.10/0.43 % SZS output start CNFRefutation
% See solution above
% 0.10/0.44 % Parsed axioms : 23
% 0.10/0.44 % Removed by relevancy pruning/SinE : 0
% 0.10/0.44 % Initial clauses : 23
% 0.10/0.44 % Removed in clause preprocessing : 2
% 0.10/0.44 % Initial clauses in saturation : 21
% 0.10/0.44 % Processed clauses : 90
% 0.10/0.44 % ...of these trivial : 18
% 0.10/0.44 % ...subsumed : 19
% 0.10/0.44 % ...remaining for further processing : 53
% 0.10/0.44 % Other redundant clauses eliminated : 0
% 0.10/0.44 % Clauses deleted for lack of memory : 0
% 0.10/0.44 % Backward-subsumed : 0
% 0.10/0.44 % Backward-rewritten : 10
% 0.10/0.44 % Generated clauses : 487
% 0.10/0.44 % ...of the previous two non-redundant : 292
% 0.10/0.44 % ...aggressively subsumed : 0
% 0.10/0.44 % Contextual simplify-reflections : 0
% 0.10/0.44 % Paramodulations : 487
% 0.10/0.44 % Factorizations : 0
% 0.10/0.44 % NegExts : 0
% 0.10/0.44 % Equation resolutions : 0
% 0.10/0.44 % Disequality decompositions : 0
% 0.10/0.44 % Total rewrite steps : 622
% 0.10/0.44 % ...of those cached : 397
% 0.10/0.44 % Propositional unsat checks : 0
% 0.10/0.44 % Propositional check models : 0
% 0.10/0.44 % Propositional check unsatisfiable : 0
% 0.10/0.44 % Propositional clauses : 0
% 0.10/0.44 % Propositional clauses after purity: 0
% 0.10/0.44 % Propositional unsat core size : 0
% 0.10/0.44 % Propositional preprocessing time : 0.000
% 0.10/0.44 % Propositional encoding time : 0.000
% 0.10/0.44 % Propositional solver time : 0.000
% 0.10/0.44 % Success case prop preproc time : 0.000
% 0.10/0.44 % Success case prop encoding time : 0.000
% 0.10/0.44 % Success case prop solver time : 0.000
% 0.10/0.44 % Current number of processed clauses : 26
% 0.10/0.44 % Positive orientable unit clauses : 23
% 0.10/0.44 % Positive unorientable unit clauses: 3
% 0.10/0.44 % Negative unit clauses : 0
% 0.10/0.44 % Non-unit-clauses : 0
% 0.10/0.44 % Current number of unprocessed clauses: 234
% 0.10/0.44 % ...number of literals in the above : 234
% 0.10/0.44 % Current number of archived formulas : 0
% 0.10/0.44 % Current number of archived clauses : 29
% 0.10/0.44 % Clause-clause subsumption calls (NU) : 0
% 0.10/0.44 % Rec. Clause-clause subsumption calls : 0
% 0.10/0.44 % Non-unit clause-clause subsumptions : 0
% 0.10/0.44 % Unit Clause-clause subsumption calls : 4
% 0.10/0.44 % Rewrite failures with RHS unbound : 0
% 0.10/0.44 % BW rewrite match attempts : 78
% 0.10/0.44 % BW rewrite match successes : 56
% 0.10/0.44 % Condensation attempts : 0
% 0.10/0.44 % Condensation successes : 0
% 0.10/0.44 % Termbank termtop insertions : 4423
% 0.10/0.44 % Search garbage collected termcells : 2
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.008 s
% 0.10/0.44 % System time : 0.001 s
% 0.10/0.44 % Total time : 0.009 s
% 0.10/0.44 % Maximum resident set size: 3648 pages
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.026 s
% 0.10/0.44 % System time : 0.015 s
% 0.10/0.44 % Total time : 0.041 s
% 0.10/0.44 % Maximum resident set size: 4608 pages
% 0.10/0.44 % E exiting
%------------------------------------------------------------------------------