%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM003-1 : 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 : n015.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 131.66s 24.82s
% Output : CNFRefutation 131.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 56 ( 21 unt; 0 nHn; 37 RR)
% Number of literals : 108 ( 0 equ; 56 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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 : 156 ( 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(addition_inverts_subtraction1,axiom,
equalish(subtract(add(X1,X2),X2),X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/NUM002-0.ax',subtract_substitution1) ).
cnf(commutativity1,axiom,
equalish(add(subtract(X1,X2),X3),subtract(add(X1,X3),X2)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/NUM002-0.ax',subtract_substitution2) ).
cnf(addition_inverts_subtraction2,axiom,
equalish(X1,subtract(add(X1,X2),X2)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM002-0.ax',addition_inverts_subtraction2) ).
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(reflexivity,axiom,
equalish(X1,X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/NUM002-0.ax',add_substitution2) ).
cnf(add_substitution1,axiom,
( ~ equalish(X3,add(X1,X4))
| ~ equalish(X1,X2)
| equalish(X3,add(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM002-0.ax',add_substitution1) ).
cnf(prove_equation,negated_conjecture,
~ equalish(add(a,subtract(b,c)),add(subtract(a,c),b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
cnf(commutativity2,axiom,
equalish(subtract(add(X1,X2),X3),add(subtract(X1,X3),X2)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM002-0.ax',commutativity2) ).
cnf(c_0_12,plain,
( ~ equalish(X2,X3)
| ~ equalish(X1,X2)
| equalish(X1,X3) ),
inference(fof_simplification,[status(thm)],[transitivity]) ).
cnf(c_0_13,plain,
( ~ equalish(X2,X3)
| ~ equalish(X1,X2)
| equalish(X1,X3) ),
c_0_12 ).
cnf(c_0_14,axiom,
equalish(subtract(add(X1,X2),X2),X1),
addition_inverts_subtraction1 ).
cnf(c_0_15,plain,
( ~ equalish(X3,subtract(X1,X4))
| ~ equalish(X1,X2)
| equalish(X3,subtract(X2,X4)) ),
inference(fof_simplification,[status(thm)],[subtract_substitution1]) ).
cnf(c_0_16,plain,
( ~ equalish(X1,subtract(add(X2,X3),X3))
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
equalish(add(subtract(X1,X2),X3),subtract(add(X1,X3),X2)),
commutativity1 ).
cnf(c_0_18,plain,
( ~ equalish(X3,subtract(X4,X1))
| ~ equalish(X1,X2)
| equalish(X3,subtract(X4,X2)) ),
inference(fof_simplification,[status(thm)],[subtract_substitution2]) ).
cnf(c_0_19,plain,
( ~ equalish(X3,subtract(X1,X4))
| ~ equalish(X1,X2)
| equalish(X3,subtract(X2,X4)) ),
c_0_15 ).
cnf(c_0_20,axiom,
equalish(X1,subtract(add(X1,X2),X2)),
addition_inverts_subtraction2 ).
cnf(c_0_21,plain,
equalish(add(subtract(X1,X2),X2),X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( ~ equalish(X3,subtract(X4,X1))
| ~ equalish(X1,X2)
| equalish(X3,subtract(X4,X2)) ),
c_0_18 ).
cnf(c_0_23,plain,
( ~ equalish(add(X1,X3),X2)
| equalish(X1,subtract(X2,X3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( ~ equalish(X1,add(subtract(X2,X3),X3))
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
cnf(c_0_25,axiom,
equalish(add(X1,X2),add(X2,X1)),
commutativity_of_addition ).
cnf(c_0_26,axiom,
equalish(X1,X1),
reflexivity ).
cnf(c_0_27,plain,
( ~ equalish(X4,X3)
| ~ equalish(add(X1,X4),X2)
| equalish(X1,subtract(X2,X3)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
equalish(add(X1,subtract(X2,X1)),X2),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
( ~ equalish(X1,X3)
| equalish(subtract(X1,X2),subtract(X3,X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_30,plain,
( ~ equalish(subtract(X2,X1),X3)
| equalish(X1,subtract(X2,X3)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
( ~ equalish(X1,add(X3,X2))
| equalish(subtract(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_29]) ).
cnf(c_0_32,plain,
( ~ equalish(X3,add(X4,X1))
| ~ equalish(X1,X2)
| equalish(X3,add(X4,X2)) ),
inference(fof_simplification,[status(thm)],[add_substitution2]) ).
cnf(c_0_33,plain,
( ~ equalish(X2,add(X3,X1))
| equalish(X1,subtract(X2,X3)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
( ~ equalish(X3,add(X4,X1))
| ~ equalish(X1,X2)
| equalish(X3,add(X4,X2)) ),
c_0_32 ).
cnf(c_0_35,plain,
( ~ equalish(add(X2,X3),add(X3,X1))
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_33]) ).
cnf(c_0_36,plain,
( ~ equalish(X1,X3)
| equalish(add(X1,X2),add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_25]) ).
cnf(c_0_37,plain,
( ~ equalish(X1,add(X3,subtract(X2,X3)))
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_38,plain,
( ~ equalish(X2,X3)
| equalish(add(X1,X2),add(X1,X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_26]) ).
cnf(c_0_39,plain,
( ~ equalish(X3,add(X1,X4))
| ~ equalish(X1,X2)
| equalish(X3,add(X2,X4)) ),
inference(fof_simplification,[status(thm)],[add_substitution1]) ).
cnf(c_0_40,plain,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
~ equalish(add(a,subtract(b,c)),add(subtract(a,c),b)),
inference(fof_simplification,[status(thm)],[prove_equation]) ).
cnf(c_0_42,plain,
( ~ equalish(X2,subtract(X3,X1))
| equalish(add(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,axiom,
equalish(subtract(add(X1,X2),X3),add(subtract(X1,X3),X2)),
commutativity2 ).
cnf(c_0_44,plain,
( ~ equalish(X4,X2)
| ~ equalish(add(X1,X3),X4)
| equalish(X1,subtract(X2,X3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_45,plain,
( ~ equalish(X3,add(X1,X4))
| ~ equalish(X1,X2)
| equalish(X3,add(X2,X4)) ),
c_0_39 ).
cnf(c_0_46,plain,
equalish(X1,add(subtract(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_40,c_0_21]) ).
cnf(c_0_47,negated_conjecture,
~ equalish(add(a,subtract(b,c)),add(subtract(a,c),b)),
c_0_41 ).
cnf(c_0_48,plain,
( ~ equalish(X2,add(subtract(X4,X1),X3))
| equalish(add(X1,subtract(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_42,c_0_31]) ).
cnf(c_0_49,plain,
( ~ equalish(X1,subtract(add(X2,X4),X3))
| equalish(X1,add(subtract(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_13,c_0_43]) ).
cnf(c_0_50,plain,
( ~ equalish(add(X3,X1),X2)
| equalish(X1,subtract(X2,X3)) ),
inference(spm,[status(thm)],[c_0_44,c_0_25]) ).
cnf(c_0_51,plain,
( ~ equalish(subtract(X1,X3),X2)
| equalish(X1,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,negated_conjecture,
~ equalish(b,add(subtract(add(subtract(a,c),b),a),c)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,plain,
( ~ equalish(add(X3,X1),add(X2,X4))
| equalish(X1,add(subtract(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,plain,
equalish(add(X1,X2),add(add(subtract(X1,X3),X2),X3)),
inference(spm,[status(thm)],[c_0_51,c_0_43]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.40 % Computer : n015.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.13/5.40 % CPULimit : 300
% 0.13/5.40 % WCLimit : 300
% 0.13/5.40 % DateTime : Mon Sep 21 02:01:10 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.47 Running first-order theorem proving
% 0.13/5.47 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
% 131.66/24.82 % Version: 3.5.1
% 131.66/24.82 % Preprocessing class: FSMSSMSSSSSNFFN.
% 131.66/24.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 131.66/24.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 131.66/24.82 % Starting new_bool_3 with 300s (1) cores
% 131.66/24.82 % Starting new_bool_1 with 300s (1) cores
% 131.66/24.82 % Starting sh5l with 300s (1) cores
% 131.66/24.82 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 321932 completed with status 0
% 131.66/24.82 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 131.66/24.82 % Preprocessing class: FSMSSMSSSSSNFFN.
% 131.66/24.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 131.66/24.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 131.66/24.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 131.66/24.82 % No SInE strategy applied
% 131.66/24.82 % Search class: FHUNM-FFSF22-SFFFFFNN
% 131.66/24.82 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 131.66/24.82 % Starting SubtermCWHack with 136s (1) cores
% 131.66/24.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 131.66/24.82 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 131.66/24.82 % Starting new_bool_3 with 136s (1) cores
% 131.66/24.82 % Starting new_bool_1 with 136s (1) cores
% 131.66/24.82 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 321938 completed with status 0
% 131.66/24.82 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 131.66/24.82 % Preprocessing class: FSMSSMSSSSSNFFN.
% 131.66/24.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 131.66/24.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 131.66/24.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 131.66/24.82 % No SInE strategy applied
% 131.66/24.82 % Search class: FHUNM-FFSF22-SFFFFFNN
% 131.66/24.82 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 131.66/24.82 % Starting SubtermCWHack with 136s (1) cores
% 131.66/24.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 131.66/24.82 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 131.66/24.82 % Preprocessing time : 0.002 s
% 131.66/24.82 % Presaturation interreduction done
% 131.66/24.82
% 131.66/24.82 % Proof found!
% 131.66/24.82 % SZS status Unsatisfiable
% 131.66/24.82 % SZS output start CNFRefutation
% See solution above
% 131.66/24.82 % Parsed axioms : 13
% 131.66/24.82 % Removed by relevancy pruning/SinE : 0
% 131.66/24.82 % Initial clauses : 13
% 131.66/24.82 % Removed in clause preprocessing : 0
% 131.66/24.82 % Initial clauses in saturation : 13
% 131.66/24.82 % Processed clauses : 24734
% 131.66/24.82 % ...of these trivial : 245
% 131.66/24.82 % ...subsumed : 21550
% 131.66/24.82 % ...remaining for further processing : 2939
% 131.66/24.82 % Other redundant clauses eliminated : 0
% 131.66/24.82 % Clauses deleted for lack of memory : 0
% 131.66/24.82 % Backward-subsumed : 5
% 131.66/24.82 % Backward-rewritten : 0
% 131.66/24.82 % Generated clauses : 942819
% 131.66/24.82 % ...of the previous two non-redundant : 922428
% 131.66/24.82 % ...aggressively subsumed : 0
% 131.66/24.82 % Contextual simplify-reflections : 4
% 131.66/24.82 % Paramodulations : 942819
% 131.66/24.82 % Factorizations : 0
% 131.66/24.82 % NegExts : 0
% 131.66/24.82 % Equation resolutions : 0
% 131.66/24.82 % Disequality decompositions : 0
% 131.66/24.82 % Total rewrite steps : 30508
% 131.66/24.82 % ...of those cached : 29623
% 131.66/24.82 % Propositional unsat checks : 0
% 131.66/24.82 % Propositional check models : 0
% 131.66/24.82 % Propositional check unsatisfiable : 0
% 131.66/24.82 % Propositional clauses : 0
% 131.66/24.82 % Propositional clauses after purity: 0
% 131.66/24.82 % Propositional unsat core size : 0
% 131.66/24.82 % Propositional preprocessing time : 0.000
% 131.66/24.82 % Propositional encoding time : 0.000
% 131.66/24.82 % Propositional solver time : 0.000
% 131.66/24.82 % Success case prop preproc time : 0.000
% 131.66/24.82 % Success case prop encoding time : 0.000
% 131.66/24.82 % Success case prop solver time : 0.000
% 131.66/24.82 % Current number of processed clauses : 2921
% 131.66/24.82 % Positive orientable unit clauses : 346
% 131.66/24.82 % Positive unorientable unit clauses: 0
% 131.66/24.82 % Negative unit clauses : 37
% 131.66/24.82 % Non-unit-clauses : 2538
% 131.66/24.82 % Current number of unprocessed clauses: 897708
% 131.66/24.82 % ...number of literals in the above : 2256315
% 131.66/24.82 % Current number of archived formulas : 0
% 131.66/24.82 % Current number of archived clauses : 18
% 131.66/24.82 % Clause-clause subsumption calls (NU) : 1491167
% 131.66/24.82 % Rec. Clause-clause subsumption calls : 1483568
% 131.66/24.82 % Non-unit clause-clause subsumptions : 21451
% 131.66/24.82 % Unit Clause-clause subsumption calls : 23548
% 131.66/24.82 % Rewrite failures with RHS unbound : 0
% 131.66/24.82 % BW rewrite match attempts : 18256
% 131.66/24.82 % BW rewrite match successes : 0
% 131.66/24.82 % Condensation attempts : 0
% 131.66/24.82 % Condensation successes : 0
% 131.66/24.82 % Termbank termtop insertions : 11544524
% 131.66/24.82 % Search garbage collected termcells : 24
% 131.66/24.82
% 131.66/24.82 % -------------------------------------------------
% 131.66/24.82 % User time : 18.084 s
% 131.66/24.82 % System time : 0.745 s
% 131.66/24.82 % Total time : 18.829 s
% 131.66/24.82 % Maximum resident set size: 3644 pages
% 131.66/24.82
% 131.66/24.82 % -------------------------------------------------
% 131.66/24.82 % User time : 89.393 s
% 131.66/24.82 % System time : 3.930 s
% 131.66/24.82 % Total time : 93.323 s
% 131.66/24.82 % Maximum resident set size: 4608 pages
% 131.66/24.82 % E exiting
%------------------------------------------------------------------------------