%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM001-1 : 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 : n007.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 01:44:13 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 21 ( 12 unt; 0 nHn; 13 RR)
% Number of literals : 36 ( 0 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity,axiom,
( ~ equalish(X2,X3)
| ~ equalish(X1,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM002-0.ax',transitivity) ).
cnf(add_substitution2,axiom,
( ~ equalish(X3,add(X4,X1))
| ~ equalish(X1,X2)
| equalish(X3,add(X4,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM002-0.ax',add_substitution2) ).
cnf(commutativity_of_addition,axiom,
equalish(add(X1,X2),add(X2,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM002-0.ax',commutativity_of_addition) ).
cnf(associativity_of_addition,axiom,
equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM002-0.ax',associativity_of_addition) ).
cnf(prove_equation,negated_conjecture,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
cnf(c_0_5,plain,
( ~ equalish(X2,X3)
| ~ equalish(X1,X2)
| equalish(X1,X3) ),
inference(fof_simplification,[status(thm)],[transitivity]) ).
cnf(c_0_6,plain,
( ~ equalish(X3,add(X4,X1))
| ~ equalish(X1,X2)
| equalish(X3,add(X4,X2)) ),
inference(fof_simplification,[status(thm)],[add_substitution2]) ).
cnf(c_0_7,plain,
( ~ equalish(X2,X3)
| ~ equalish(X1,X2)
| equalish(X1,X3) ),
c_0_5 ).
cnf(c_0_8,axiom,
equalish(add(X1,X2),add(X2,X1)),
commutativity_of_addition ).
cnf(c_0_9,plain,
( ~ equalish(X3,add(X4,X1))
| ~ equalish(X1,X2)
| equalish(X3,add(X4,X2)) ),
c_0_6 ).
cnf(c_0_10,plain,
( ~ equalish(X1,add(X3,X2))
| equalish(X1,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,axiom,
equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3)),
associativity_of_addition ).
cnf(c_0_12,plain,
( ~ equalish(X1,add(X2,add(X4,X3)))
| equalish(X1,add(X2,add(X3,X4))) ),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_13,plain,
equalish(add(X1,add(X2,X3)),add(X3,add(X1,X2))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
equalish(add(X1,add(X2,X3)),add(X3,add(X2,X1))),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,negated_conjecture,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
inference(fof_simplification,[status(thm)],[prove_equation]) ).
cnf(c_0_16,plain,
( ~ equalish(X1,add(X4,add(X3,X2)))
| equalish(X1,add(X2,add(X3,X4))) ),
inference(spm,[status(thm)],[c_0_7,c_0_14]) ).
cnf(c_0_17,plain,
equalish(add(add(X1,X2),X3),add(X3,add(X2,X1))),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
cnf(c_0_18,negated_conjecture,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
c_0_15 ).
cnf(c_0_19,plain,
equalish(add(add(X1,X2),X3),add(X1,add(X2,X3))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 01:55:35 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.44 % Version: 3.5.1
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.44 % Starting sh5l with 300s (1) cores
% 0.12/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4123444 completed with status 0
% 0.12/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.44 % No SInE strategy applied
% 0.12/0.44 % Search class: FHUNM-FFSF22-SFFFFFNN
% 0.12/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.12/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.12/0.44 % new_bool_3 with pid 4123453 completed with status 0
% 0.12/0.44 % Result found by new_bool_3
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.44 % No SInE strategy applied
% 0.12/0.44 % Search class: FHUNM-FFSF22-SFFFFFNN
% 0.12/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.12/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.44 % Preprocessing time : 0.001 s
% 0.12/0.44 % Presaturation interreduction done
% 0.12/0.44
% 0.12/0.44 % Proof found!
% 0.12/0.44 % SZS status Unsatisfiable
% 0.12/0.44 % SZS output start CNFRefutation
% See solution above
% 0.12/0.44 % Parsed axioms : 13
% 0.12/0.44 % Removed by relevancy pruning/SinE : 0
% 0.12/0.44 % Initial clauses : 13
% 0.12/0.44 % Removed in clause preprocessing : 0
% 0.12/0.44 % Initial clauses in saturation : 13
% 0.12/0.44 % Processed clauses : 191
% 0.12/0.44 % ...of these trivial : 20
% 0.12/0.44 % ...subsumed : 2
% 0.12/0.44 % ...remaining for further processing : 169
% 0.12/0.44 % Other redundant clauses eliminated : 0
% 0.12/0.44 % Clauses deleted for lack of memory : 0
% 0.12/0.44 % Backward-subsumed : 0
% 0.12/0.44 % Backward-rewritten : 1
% 0.12/0.44 % Generated clauses : 3218
% 0.12/0.44 % ...of the previous two non-redundant : 2861
% 0.12/0.44 % ...aggressively subsumed : 0
% 0.12/0.44 % Contextual simplify-reflections : 0
% 0.12/0.44 % Paramodulations : 3218
% 0.12/0.44 % Factorizations : 0
% 0.12/0.44 % NegExts : 0
% 0.12/0.44 % Equation resolutions : 0
% 0.12/0.44 % Disequality decompositions : 0
% 0.12/0.44 % Total rewrite steps : 308
% 0.12/0.44 % ...of those cached : 242
% 0.12/0.44 % Propositional unsat checks : 0
% 0.12/0.44 % Propositional check models : 0
% 0.12/0.44 % Propositional check unsatisfiable : 0
% 0.12/0.44 % Propositional clauses : 0
% 0.12/0.44 % Propositional clauses after purity: 0
% 0.12/0.44 % Propositional unsat core size : 0
% 0.12/0.44 % Propositional preprocessing time : 0.000
% 0.12/0.44 % Propositional encoding time : 0.000
% 0.12/0.44 % Propositional solver time : 0.000
% 0.12/0.44 % Success case prop preproc time : 0.000
% 0.12/0.44 % Success case prop encoding time : 0.000
% 0.12/0.44 % Success case prop solver time : 0.000
% 0.12/0.44 % Current number of processed clauses : 155
% 0.12/0.44 % Positive orientable unit clauses : 48
% 0.12/0.44 % Positive unorientable unit clauses: 0
% 0.12/0.44 % Negative unit clauses : 0
% 0.12/0.44 % Non-unit-clauses : 107
% 0.12/0.44 % Current number of unprocessed clauses: 2696
% 0.12/0.44 % ...number of literals in the above : 2822
% 0.12/0.44 % Current number of archived formulas : 0
% 0.12/0.44 % Current number of archived clauses : 14
% 0.12/0.44 % Clause-clause subsumption calls (NU) : 1600
% 0.12/0.44 % Rec. Clause-clause subsumption calls : 1600
% 0.12/0.44 % Non-unit clause-clause subsumptions : 2
% 0.12/0.44 % Unit Clause-clause subsumption calls : 134
% 0.12/0.44 % Rewrite failures with RHS unbound : 0
% 0.12/0.44 % BW rewrite match attempts : 116
% 0.12/0.44 % BW rewrite match successes : 1
% 0.12/0.44 % Condensation attempts : 0
% 0.12/0.44 % Condensation successes : 0
% 0.12/0.44 % Termbank termtop insertions : 32815
% 0.12/0.44 % Search garbage collected termcells : 24
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.033 s
% 0.12/0.44 % System time : 0.009 s
% 0.12/0.44 % Total time : 0.042 s
% 0.12/0.44 % Maximum resident set size: 3644 pages
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.178 s
% 0.12/0.44 % System time : 0.030 s
% 0.12/0.44 % Total time : 0.209 s
% 0.12/0.44 % Maximum resident set size: 4864 pages
% 0.12/0.44 % E exiting
%------------------------------------------------------------------------------