%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM004-1 : 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 : 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 01:44:13 PM UTC 2026
% Result : Unsatisfiable 0.15s 20.78s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of clauses : 47 ( 22 unt; 0 nHn; 29 RR)
% Number of literals : 85 ( 0 equ; 44 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 : 118 ( 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(prove_equation,negated_conjecture,
~ equalish(subtract(add(a,b),c),add(a,subtract(b,c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
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(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(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,negated_conjecture,
~ equalish(subtract(add(a,b),c),add(a,subtract(b,c))),
inference(fof_simplification,[status(thm)],[prove_equation]) ).
cnf(c_0_30,plain,
( ~ equalish(subtract(X2,X1),X3)
| equalish(X1,subtract(X2,X3)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
( ~ equalish(X1,add(X3,X2))
| equalish(subtract(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_28]) ).
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,negated_conjecture,
~ equalish(subtract(add(a,b),c),add(a,subtract(b,c))),
c_0_29 ).
cnf(c_0_34,axiom,
equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3)),
associativity_of_addition ).
cnf(c_0_35,plain,
( ~ equalish(X2,add(X3,X1))
| equalish(X1,subtract(X2,X3)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
( ~ equalish(X3,add(X4,X1))
| ~ equalish(X1,X2)
| equalish(X3,add(X4,X2)) ),
c_0_32 ).
cnf(c_0_37,negated_conjecture,
~ equalish(add(a,b),add(add(a,subtract(b,c)),c)),
inference(spm,[status(thm)],[c_0_33,c_0_31]) ).
cnf(c_0_38,plain,
( ~ equalish(X1,add(X2,add(X3,X4)))
| equalish(X1,add(add(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_12,c_0_34]) ).
cnf(c_0_39,plain,
( ~ equalish(add(X2,X3),add(X3,X1))
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_35]) ).
cnf(c_0_40,plain,
( ~ equalish(X3,X4)
| equalish(add(X1,add(X2,X3)),add(add(X1,X2),X4)) ),
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_41,negated_conjecture,
~ equalish(add(a,b),add(a,add(subtract(b,c),c))),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
( ~ equalish(X2,X3)
| equalish(add(X1,X2),add(X1,X3)) ),
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_43,plain,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
~ equalish(b,add(subtract(b,c),c)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
equalish(X1,add(subtract(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_43,c_0_20]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.15/20.70 % CPULimit : 300
% 0.15/20.70 % WCLimit : 300
% 0.15/20.70 % DateTime : Mon Sep 21 01:58:02 UTC 2026
% 0.15/20.70 % CPUTime :
% 0.15/20.70 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/20.75 Running first-order theorem proving
% 0.15/20.75 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
% 0.15/20.78 % Version: 3.5.1
% 0.15/20.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/20.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/20.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/20.78 % Starting new_bool_3 with 300s (1) cores
% 0.15/20.78 % Starting new_bool_1 with 300s (1) cores
% 0.15/20.78 % Starting sh5l with 300s (1) cores
% 0.15/20.78 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3914543 completed with status 0
% 0.15/20.78 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/20.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/20.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/20.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/20.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/20.78 % No SInE strategy applied
% 0.15/20.78 % Search class: FHUNM-FFSF22-SFFFFFNN
% 0.15/20.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/20.78 % Starting SubtermCWHack with 136s (1) cores
% 0.15/20.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/20.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/20.78 % Starting new_bool_3 with 136s (1) cores
% 0.15/20.78 % Starting new_bool_1 with 136s (1) cores
% 0.15/20.78 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3914548 completed with status 0
% 0.15/20.78 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/20.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/20.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/20.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/20.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/20.78 % No SInE strategy applied
% 0.15/20.78 % Search class: FHUNM-FFSF22-SFFFFFNN
% 0.15/20.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/20.78 % Starting SubtermCWHack with 136s (1) cores
% 0.15/20.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/20.78 % Preprocessing time : 0.001 s
% 0.15/20.78 % Presaturation interreduction done
% 0.15/20.78
% 0.15/20.78 % Proof found!
% 0.15/20.78 % SZS status Unsatisfiable
% 0.15/20.78 % SZS output start CNFRefutation
% See solution above
% 0.15/20.78 % Parsed axioms : 13
% 0.15/20.78 % Removed by relevancy pruning/SinE : 0
% 0.15/20.78 % Initial clauses : 13
% 0.15/20.78 % Removed in clause preprocessing : 0
% 0.15/20.78 % Initial clauses in saturation : 13
% 0.15/20.78 % Processed clauses : 106
% 0.15/20.78 % ...of these trivial : 0
% 0.15/20.78 % ...subsumed : 22
% 0.15/20.78 % ...remaining for further processing : 84
% 0.15/20.78 % Other redundant clauses eliminated : 0
% 0.15/20.78 % Clauses deleted for lack of memory : 0
% 0.15/20.78 % Backward-subsumed : 0
% 0.15/20.78 % Backward-rewritten : 1
% 0.15/20.78 % Generated clauses : 747
% 0.15/20.78 % ...of the previous two non-redundant : 659
% 0.15/20.78 % ...aggressively subsumed : 0
% 0.15/20.78 % Contextual simplify-reflections : 0
% 0.15/20.78 % Paramodulations : 747
% 0.15/20.78 % Factorizations : 0
% 0.15/20.78 % NegExts : 0
% 0.15/20.78 % Equation resolutions : 0
% 0.15/20.78 % Disequality decompositions : 0
% 0.15/20.78 % Total rewrite steps : 53
% 0.15/20.78 % ...of those cached : 39
% 0.15/20.78 % Propositional unsat checks : 0
% 0.15/20.78 % Propositional check models : 0
% 0.15/20.78 % Propositional check unsatisfiable : 0
% 0.15/20.78 % Propositional clauses : 0
% 0.15/20.78 % Propositional clauses after purity: 0
% 0.15/20.78 % Propositional unsat core size : 0
% 0.15/20.78 % Propositional preprocessing time : 0.000
% 0.15/20.78 % Propositional encoding time : 0.000
% 0.15/20.78 % Propositional solver time : 0.000
% 0.15/20.78 % Success case prop preproc time : 0.000
% 0.15/20.78 % Success case prop encoding time : 0.000
% 0.15/20.78 % Success case prop solver time : 0.000
% 0.15/20.78 % Current number of processed clauses : 70
% 0.15/20.78 % Positive orientable unit clauses : 12
% 0.15/20.78 % Positive unorientable unit clauses: 0
% 0.15/20.78 % Negative unit clauses : 3
% 0.15/20.78 % Non-unit-clauses : 55
% 0.15/20.78 % Current number of unprocessed clauses: 579
% 0.15/20.78 % ...number of literals in the above : 1371
% 0.15/20.78 % Current number of archived formulas : 0
% 0.15/20.78 % Current number of archived clauses : 14
% 0.15/20.78 % Clause-clause subsumption calls (NU) : 459
% 0.15/20.78 % Rec. Clause-clause subsumption calls : 459
% 0.15/20.78 % Non-unit clause-clause subsumptions : 22
% 0.15/20.78 % Unit Clause-clause subsumption calls : 19
% 0.15/20.78 % Rewrite failures with RHS unbound : 0
% 0.15/20.78 % BW rewrite match attempts : 10
% 0.15/20.78 % BW rewrite match successes : 1
% 0.15/20.78 % Condensation attempts : 0
% 0.15/20.78 % Condensation successes : 0
% 0.15/20.78 % Termbank termtop insertions : 7997
% 0.15/20.78 % Search garbage collected termcells : 24
% 0.15/20.78
% 0.15/20.78 % -------------------------------------------------
% 0.15/20.78 % User time : 0.011 s
% 0.15/20.78 % System time : 0.006 s
% 0.15/20.78 % Total time : 0.016 s
% 0.15/20.78 % Maximum resident set size: 3644 pages
% 0.15/20.78
% 0.15/20.78 % -------------------------------------------------
% 0.15/20.78 % User time : 0.065 s
% 0.15/20.78 % System time : 0.017 s
% 0.15/20.78 % Total time : 0.083 s
% 0.15/20.78 % Maximum resident set size: 4608 pages
% 0.15/20.78 % E exiting
%------------------------------------------------------------------------------