%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM002-1 : 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 : n020.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 01:51:10 PM UTC 2026
% Result : Unsatisfiable 28.58s 14.64s
% Output : CNFRefutation 28.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of clauses : 54 ( 23 unt; 0 nHn; 33 RR)
% Number of literals : 100 ( 0 equ; 51 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 145 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity,axiom,
( ~ equalish(X2,X3)
| ~ equalish(X1,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',transitivity) ).
cnf(addition_inverts_subtraction1,axiom,
equalish(subtract(add(X1,X2),X2),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',addition_inverts_subtraction1) ).
cnf(subtract_substitution1,axiom,
( ~ equalish(X3,subtract(X1,X4))
| ~ equalish(X1,X2)
| equalish(X3,subtract(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',subtract_substitution1) ).
cnf(commutativity1,axiom,
equalish(add(subtract(X1,X2),X3),subtract(add(X1,X3),X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',commutativity1) ).
cnf(subtract_substitution2,axiom,
( ~ equalish(X3,subtract(X4,X1))
| ~ equalish(X1,X2)
| equalish(X3,subtract(X4,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',subtract_substitution2) ).
cnf(addition_inverts_subtraction2,axiom,
equalish(X1,subtract(add(X1,X2),X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',addition_inverts_subtraction2) ).
cnf(commutativity_of_addition,axiom,
equalish(add(X1,X2),add(X2,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',commutativity_of_addition) ).
cnf(reflexivity,axiom,
equalish(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',reflexivity) ).
cnf(add_substitution2,axiom,
( ~ equalish(X3,add(X4,X1))
| ~ equalish(X1,X2)
| equalish(X3,add(X4,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',add_substitution2) ).
cnf(prove_equation,negated_conjecture,
~ equalish(add(subtract(a,b),c),add(a,subtract(c,b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
cnf(associativity_of_addition,axiom,
equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',associativity_of_addition) ).
cnf(c_0_11,plain,
( ~ equalish(X2,X3)
| ~ equalish(X1,X2)
| equalish(X1,X3) ),
inference(fof_simplification,[status(thm)],[transitivity]) ).
cnf(c_0_12,plain,
( ~ equalish(X2,X3)
| ~ equalish(X1,X2)
| equalish(X1,X3) ),
c_0_11 ).
cnf(c_0_13,axiom,
equalish(subtract(add(X1,X2),X2),X1),
addition_inverts_subtraction1 ).
cnf(c_0_14,plain,
( ~ equalish(X3,subtract(X1,X4))
| ~ equalish(X1,X2)
| equalish(X3,subtract(X2,X4)) ),
inference(fof_simplification,[status(thm)],[subtract_substitution1]) ).
cnf(c_0_15,plain,
( ~ equalish(X1,subtract(add(X2,X3),X3))
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
equalish(add(subtract(X1,X2),X3),subtract(add(X1,X3),X2)),
commutativity1 ).
cnf(c_0_17,plain,
( ~ equalish(X3,subtract(X4,X1))
| ~ equalish(X1,X2)
| equalish(X3,subtract(X4,X2)) ),
inference(fof_simplification,[status(thm)],[subtract_substitution2]) ).
cnf(c_0_18,plain,
( ~ equalish(X3,subtract(X1,X4))
| ~ equalish(X1,X2)
| equalish(X3,subtract(X2,X4)) ),
c_0_14 ).
cnf(c_0_19,axiom,
equalish(X1,subtract(add(X1,X2),X2)),
addition_inverts_subtraction2 ).
cnf(c_0_20,plain,
equalish(add(subtract(X1,X2),X2),X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( ~ equalish(X3,subtract(X4,X1))
| ~ equalish(X1,X2)
| equalish(X3,subtract(X4,X2)) ),
c_0_17 ).
cnf(c_0_22,plain,
( ~ equalish(add(X1,X3),X2)
| equalish(X1,subtract(X2,X3)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ~ equalish(X1,add(subtract(X2,X3),X3))
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_24,axiom,
equalish(add(X1,X2),add(X2,X1)),
commutativity_of_addition ).
cnf(c_0_25,axiom,
equalish(X1,X1),
reflexivity ).
cnf(c_0_26,plain,
( ~ equalish(X4,X3)
| ~ equalish(add(X1,X4),X2)
| equalish(X1,subtract(X2,X3)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
equalish(add(X1,subtract(X2,X1)),X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( ~ equalish(X1,X3)
| equalish(subtract(X1,X2),subtract(X3,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_29,plain,
( ~ equalish(subtract(X2,X1),X3)
| equalish(X1,subtract(X2,X3)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,plain,
( ~ equalish(X1,add(X3,X2))
| equalish(subtract(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_28]) ).
cnf(c_0_31,plain,
( ~ equalish(X3,add(X4,X1))
| ~ equalish(X1,X2)
| equalish(X3,add(X4,X2)) ),
inference(fof_simplification,[status(thm)],[add_substitution2]) ).
cnf(c_0_32,plain,
( ~ equalish(X2,add(X3,X1))
| equalish(X1,subtract(X2,X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
( ~ equalish(X3,add(X4,X1))
| ~ equalish(X1,X2)
| equalish(X3,add(X4,X2)) ),
c_0_31 ).
cnf(c_0_34,plain,
( ~ equalish(add(X2,X3),add(X3,X1))
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_32]) ).
cnf(c_0_35,plain,
( ~ equalish(X1,X3)
| equalish(add(X1,X2),add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_33,c_0_24]) ).
cnf(c_0_36,plain,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,plain,
equalish(X1,subtract(X2,subtract(X2,X1))),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_38,plain,
equalish(subtract(X1,subtract(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,negated_conjecture,
~ equalish(add(subtract(a,b),c),add(a,subtract(c,b))),
inference(fof_simplification,[status(thm)],[prove_equation]) ).
cnf(c_0_40,plain,
( ~ equalish(X1,subtract(X3,subtract(X3,X2)))
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_38]) ).
cnf(c_0_41,plain,
( ~ equalish(X2,X4)
| equalish(add(subtract(X1,X2),X3),subtract(add(X1,X3),X4)) ),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_42,plain,
( ~ equalish(X1,add(X3,X2))
| equalish(X1,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_24]) ).
cnf(c_0_43,axiom,
equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3)),
associativity_of_addition ).
cnf(c_0_44,negated_conjecture,
~ equalish(add(subtract(a,b),c),add(a,subtract(c,b))),
c_0_39 ).
cnf(c_0_45,plain,
( ~ equalish(X2,subtract(add(X1,X3),X4))
| equalish(add(subtract(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
( ~ equalish(X4,X2)
| ~ equalish(add(X1,X3),X4)
| equalish(X1,subtract(X2,X3)) ),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_47,plain,
equalish(add(X1,add(X2,X3)),add(X3,add(X1,X2))),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
~ equalish(b,subtract(add(a,c),add(a,subtract(c,b)))),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
( ~ equalish(add(X4,add(X1,X3)),X2)
| equalish(X1,subtract(X2,add(X3,X4))) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,plain,
( ~ equalish(X4,X3)
| ~ equalish(X1,add(X4,X2))
| equalish(X1,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_35]) ).
cnf(c_0_51,negated_conjecture,
~ equalish(add(subtract(c,b),add(b,a)),add(a,c)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,plain,
( ~ equalish(add(X1,X2),X4)
| equalish(add(X1,add(X2,X3)),add(X3,X4)) ),
inference(spm,[status(thm)],[c_0_50,c_0_43]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/10.39 % Computer : n020.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Mon Sep 21 01:59:28 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/10.43 Running first-order theorem proving
% 0.14/10.43 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
% 28.58/14.64 % Version: 3.5.1
% 28.58/14.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 28.58/14.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 28.58/14.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 28.58/14.64 % Starting new_bool_3 with 300s (1) cores
% 28.58/14.64 % Starting new_bool_1 with 300s (1) cores
% 28.58/14.64 % Starting sh5l with 300s (1) cores
% 28.58/14.64 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1757288 completed with status 0
% 28.58/14.64 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 28.58/14.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 28.58/14.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 28.58/14.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 28.58/14.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 28.58/14.64 % No SInE strategy applied
% 28.58/14.64 % Search class: FHUNM-FFSF22-SFFFFFNN
% 28.58/14.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 28.58/14.64 % Starting SubtermCWHack with 136s (1) cores
% 28.58/14.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 28.58/14.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 28.58/14.64 % Starting new_bool_3 with 136s (1) cores
% 28.58/14.64 % Starting new_bool_1 with 136s (1) cores
% 28.58/14.64 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 1757296 completed with status 0
% 28.58/14.64 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 28.58/14.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 28.58/14.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 28.58/14.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 28.58/14.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 28.58/14.64 % No SInE strategy applied
% 28.58/14.64 % Search class: FHUNM-FFSF22-SFFFFFNN
% 28.58/14.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 28.58/14.64 % Starting SubtermCWHack with 136s (1) cores
% 28.58/14.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 28.58/14.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 28.58/14.64 % Preprocessing time : 0.001 s
% 28.58/14.64 % Presaturation interreduction done
% 28.58/14.64
% 28.58/14.64 % Proof found!
% 28.58/14.64 % SZS status Unsatisfiable
% 28.58/14.64 % SZS output start CNFRefutation
% See solution above
% 28.58/14.64 % Parsed axioms : 13
% 28.58/14.64 % Removed by relevancy pruning/SinE : 0
% 28.58/14.64 % Initial clauses : 13
% 28.58/14.64 % Removed in clause preprocessing : 0
% 28.58/14.64 % Initial clauses in saturation : 13
% 28.58/14.64 % Processed clauses : 15729
% 28.58/14.64 % ...of these trivial : 141
% 28.58/14.64 % ...subsumed : 13544
% 28.58/14.64 % ...remaining for further processing : 2044
% 28.58/14.64 % Other redundant clauses eliminated : 0
% 28.58/14.64 % Clauses deleted for lack of memory : 0
% 28.58/14.64 % Backward-subsumed : 1
% 28.58/14.64 % Backward-rewritten : 0
% 28.58/14.64 % Generated clauses : 447705
% 28.58/14.64 % ...of the previous two non-redundant : 438097
% 28.58/14.64 % ...aggressively subsumed : 0
% 28.58/14.64 % Contextual simplify-reflections : 7
% 28.58/14.64 % Paramodulations : 447705
% 28.58/14.64 % Factorizations : 0
% 28.58/14.64 % NegExts : 0
% 28.58/14.64 % Equation resolutions : 0
% 28.58/14.64 % Disequality decompositions : 0
% 28.58/14.64 % Total rewrite steps : 16139
% 28.58/14.64 % ...of those cached : 15662
% 28.58/14.64 % Propositional unsat checks : 0
% 28.58/14.64 % Propositional check models : 0
% 28.58/14.64 % Propositional check unsatisfiable : 0
% 28.58/14.64 % Propositional clauses : 0
% 28.58/14.64 % Propositional clauses after purity: 0
% 28.58/14.64 % Propositional unsat core size : 0
% 28.58/14.64 % Propositional preprocessing time : 0.000
% 28.58/14.64 % Propositional encoding time : 0.000
% 28.58/14.64 % Propositional solver time : 0.000
% 28.58/14.64 % Success case prop preproc time : 0.000
% 28.58/14.64 % Success case prop encoding time : 0.000
% 28.58/14.64 % Success case prop solver time : 0.000
% 28.58/14.64 % Current number of processed clauses : 2030
% 28.58/14.64 % Positive orientable unit clauses : 227
% 28.58/14.64 % Positive unorientable unit clauses: 0
% 28.58/14.64 % Negative unit clauses : 29
% 28.58/14.64 % Non-unit-clauses : 1774
% 28.58/14.64 % Current number of unprocessed clauses: 422379
% 28.58/14.64 % ...number of literals in the above : 1064596
% 28.58/14.64 % Current number of archived formulas : 0
% 28.58/14.64 % Current number of archived clauses : 14
% 28.58/14.64 % Clause-clause subsumption calls (NU) : 830501
% 28.58/14.64 % Rec. Clause-clause subsumption calls : 824956
% 28.58/14.64 % Non-unit clause-clause subsumptions : 13521
% 28.58/14.64 % Unit Clause-clause subsumption calls : 11246
% 28.58/14.64 % Rewrite failures with RHS unbound : 0
% 28.58/14.64 % BW rewrite match attempts : 8836
% 28.58/14.64 % BW rewrite match successes : 0
% 28.58/14.64 % Condensation attempts : 0
% 28.58/14.64 % Condensation successes : 0
% 28.58/14.64 % Termbank termtop insertions : 5387436
% 28.58/14.64 % Search garbage collected termcells : 24
% 28.58/14.64
% 28.58/14.64 % -------------------------------------------------
% 28.58/14.64 % User time : 3.732 s
% 28.58/14.64 % System time : 0.234 s
% 28.58/14.64 % Total time : 3.966 s
% 28.58/14.64 % Maximum resident set size: 3644 pages
% 28.58/14.64
% 28.58/14.64 % -------------------------------------------------
% 28.58/14.64 % User time : 19.077 s
% 28.58/14.64 % System time : 1.120 s
% 28.58/14.64 % Total time : 20.196 s
% 28.58/14.64 % Maximum resident set size: 4608 pages
% 28.58/14.64 % E exiting
%------------------------------------------------------------------------------