%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG004-3 : 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 : n017.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 02:05:27 PM UTC 2026
% Result : Unsatisfiable 65.16s 10.17s
% Output : CNFRefutation 65.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 44 ( 23 unt; 0 nHn; 32 RR)
% Number of literals : 99 ( 0 equ; 58 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 113 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity3,axiom,
( ~ product(X6,X2,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(distributivity1,axiom,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
cnf(a_times_b,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
cnf(associativity_of_addition1,axiom,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).
cnf(multiplicative_identity1,axiom,
product(additive_identity,X1,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
cnf(multiplicative_identity2,axiom,
product(X1,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
cnf(addition_is_well_defined,axiom,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(a_inverse_times_b_inverse,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
cnf(prove_c_equals_d,negated_conjecture,
~ equalish(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(c_0_13,plain,
( ~ product(X6,X2,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity3]) ).
cnf(c_0_14,plain,
( ~ product(X6,X2,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_13 ).
cnf(c_0_15,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_16,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity1]) ).
cnf(c_0_17,plain,
( ~ product(X4,X5,X2)
| ~ product(additive_identity,X5,X3)
| ~ product(additive_inverse(X4),X5,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,hypothesis,
product(a,b,c),
a_times_b ).
cnf(c_0_19,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_16 ).
cnf(c_0_20,plain,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_addition1]) ).
cnf(c_0_21,hypothesis,
( ~ product(additive_identity,b,X2)
| ~ product(additive_inverse(a),b,X1)
| sum(X1,c,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,axiom,
product(additive_identity,X1,additive_identity),
multiplicative_identity1 ).
cnf(c_0_23,plain,
( ~ product(X4,X5,X2)
| ~ product(X4,additive_identity,X3)
| ~ product(X4,additive_inverse(X5),X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_24,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_25,plain,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
c_0_20 ).
cnf(c_0_26,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_27,hypothesis,
( ~ product(additive_inverse(a),b,X1)
| sum(X1,c,additive_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( ~ product(X2,additive_identity,X4)
| ~ product(X2,additive_inverse(X3),X1)
| sum(X1,multiply(X2,X3),X4) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,axiom,
product(X1,additive_identity,additive_identity),
multiplicative_identity2 ).
cnf(c_0_30,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_31,plain,
( ~ sum(X4,X3,X2)
| ~ sum(X1,X4,additive_identity)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,hypothesis,
sum(multiply(additive_inverse(a),b),c,additive_identity),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_33,plain,
( ~ product(X2,additive_inverse(X3),X1)
| sum(X1,multiply(X2,X3),additive_identity) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
a_inverse_times_b_inverse ).
cnf(c_0_35,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| equalish(X3,X4) ),
c_0_30 ).
cnf(c_0_36,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_37,hypothesis,
( ~ sum(X1,multiply(additive_inverse(a),b),additive_identity)
| sum(X1,additive_identity,c) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,hypothesis,
sum(d,multiply(additive_inverse(a),b),additive_identity),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
~ equalish(c,d),
inference(fof_simplification,[status(thm)],[prove_c_equals_d]) ).
cnf(c_0_40,plain,
( ~ sum(X2,additive_identity,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,hypothesis,
sum(d,additive_identity,c),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
~ equalish(c,d),
c_0_39 ).
cnf(c_0_43,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 % Computer : n017.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 04:05:12 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.51 Running first-order theorem proving
% 0.19/0.51 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
% 65.16/10.17 % Version: 3.5.1
% 65.16/10.17 % Preprocessing class: FSMSSMSSSSSNFFN.
% 65.16/10.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 65.16/10.17 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 65.16/10.17 % Starting new_bool_3 with 300s (1) cores
% 65.16/10.17 % Starting new_bool_1 with 300s (1) cores
% 65.16/10.17 % Starting sh5l with 300s (1) cores
% 65.16/10.17 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1390043 completed with status 0
% 65.16/10.17 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 65.16/10.17 % Preprocessing class: FSMSSMSSSSSNFFN.
% 65.16/10.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 65.16/10.17 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 65.16/10.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 65.16/10.17 % No SInE strategy applied
% 65.16/10.17 % Search class: FHUNM-FFMF21-SFFFFFNN
% 65.16/10.17 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 65.16/10.17 % Starting SubtermCWHack with 136s (1) cores
% 65.16/10.17 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 65.16/10.17 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 65.16/10.17 % Starting G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A with 136s (1) cores
% 65.16/10.17 % Starting new_bool_3 with 136s (1) cores
% 65.16/10.17 % new_bool_3 with pid 1390051 completed with status 0
% 65.16/10.17 % Result found by new_bool_3
% 65.16/10.17 % Preprocessing class: FSMSSMSSSSSNFFN.
% 65.16/10.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 65.16/10.17 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 65.16/10.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 65.16/10.17 % No SInE strategy applied
% 65.16/10.17 % Search class: FHUNM-FFMF21-SFFFFFNN
% 65.16/10.17 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 65.16/10.17 % Starting SubtermCWHack with 136s (1) cores
% 65.16/10.17 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 65.16/10.17 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 65.16/10.17 % Starting G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A with 136s (1) cores
% 65.16/10.17 % Starting new_bool_3 with 136s (1) cores
% 65.16/10.17 % Preprocessing time : 0.001 s
% 65.16/10.17 % Presaturation interreduction done
% 65.16/10.17
% 65.16/10.17 % Proof found!
% 65.16/10.17 % SZS status Unsatisfiable
% 65.16/10.17 % SZS output start CNFRefutation
% See solution above
% 65.16/10.17 % Parsed axioms : 34
% 65.16/10.17 % Removed by relevancy pruning/SinE : 0
% 65.16/10.17 % Initial clauses : 34
% 65.16/10.17 % Removed in clause preprocessing : 0
% 65.16/10.17 % Initial clauses in saturation : 34
% 65.16/10.17 % Processed clauses : 18427
% 65.16/10.17 % ...of these trivial : 4537
% 65.16/10.17 % ...subsumed : 4952
% 65.16/10.17 % ...remaining for further processing : 8938
% 65.16/10.17 % Other redundant clauses eliminated : 0
% 65.16/10.17 % Clauses deleted for lack of memory : 0
% 65.16/10.17 % Backward-subsumed : 856
% 65.16/10.17 % Backward-rewritten : 583
% 65.16/10.17 % Generated clauses : 765243
% 65.16/10.17 % ...of the previous two non-redundant : 661675
% 65.16/10.17 % ...aggressively subsumed : 0
% 65.16/10.17 % Contextual simplify-reflections : 0
% 65.16/10.17 % Paramodulations : 765243
% 65.16/10.17 % Factorizations : 0
% 65.16/10.17 % NegExts : 0
% 65.16/10.17 % Equation resolutions : 0
% 65.16/10.17 % Disequality decompositions : 0
% 65.16/10.17 % Total rewrite steps : 119228
% 65.16/10.17 % ...of those cached : 102985
% 65.16/10.17 % Propositional unsat checks : 1
% 65.16/10.17 % Propositional check models : 0
% 65.16/10.17 % Propositional check unsatisfiable : 0
% 65.16/10.17 % Propositional clauses : 0
% 65.16/10.17 % Propositional clauses after purity: 0
% 65.16/10.17 % Propositional unsat core size : 0
% 65.16/10.17 % Propositional preprocessing time : 0.000
% 65.16/10.17 % Propositional encoding time : 0.258
% 65.16/10.17 % Propositional solver time : 0.434
% 65.16/10.17 % Success case prop preproc time : 0.000
% 65.16/10.17 % Success case prop encoding time : 0.000
% 65.16/10.17 % Success case prop solver time : 0.000
% 65.16/10.17 % Current number of processed clauses : 7465
% 65.16/10.17 % Positive orientable unit clauses : 2239
% 65.16/10.17 % Positive unorientable unit clauses: 0
% 65.16/10.17 % Negative unit clauses : 1
% 65.16/10.17 % Non-unit-clauses : 5225
% 65.16/10.17 % Current number of unprocessed clauses: 639549
% 65.16/10.17 % ...number of literals in the above : 827179
% 65.16/10.17 % Current number of archived formulas : 0
% 65.16/10.17 % Current number of archived clauses : 1473
% 65.16/10.17 % Clause-clause subsumption calls (NU) : 3417015
% 65.16/10.17 % Rec. Clause-clause subsumption calls : 2593838
% 65.16/10.17 % Non-unit clause-clause subsumptions : 5808
% 65.16/10.17 % Unit Clause-clause subsumption calls : 8137
% 65.16/10.17 % Rewrite failures with RHS unbound : 0
% 65.16/10.17 % BW rewrite match attempts : 51883
% 65.16/10.17 % BW rewrite match successes : 583
% 65.16/10.17 % Condensation attempts : 0
% 65.16/10.17 % Condensation successes : 0
% 65.16/10.17 % Termbank termtop insertions : 11071913
% 65.16/10.17 % Search garbage collected termcells : 95
% 65.16/10.17
% 65.16/10.17 % -------------------------------------------------
% 65.16/10.17 % User time : 8.859 s
% 65.16/10.17 % System time : 0.423 s
% 65.16/10.17 % Total time : 9.282 s
% 65.16/10.17 % Maximum resident set size: 3656 pages
% 65.16/10.17
% 65.16/10.17 % -------------------------------------------------
% 65.16/10.17 % User time : 44.199 s
% 65.16/10.17 % System time : 1.985 s
% 65.16/10.17 % Total time : 46.184 s
% 65.16/10.17 % Maximum resident set size: 4864 pages
% 65.16/10.17 % E exiting
%------------------------------------------------------------------------------