%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ROB023-1 : 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 02:06:41 PM UTC 2026
% Result : Unsatisfiable 0.59s 0.50s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 5 RR)
% Number of literals : 29 ( 28 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(robbins_axiom,axiom,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',robbins_axiom) ).
cnf(x_plus_x_is_x,hypothesis,
add(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_x_is_x) ).
cnf(associativity_of_add,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',associativity_of_add) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',commutativity_of_add) ).
cnf(prove_huntingtons_axiom,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_huntingtons_axiom) ).
cnf(c_0_5,axiom,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
robbins_axiom ).
cnf(c_0_6,hypothesis,
add(X1,X1) = X1,
x_plus_x_is_x ).
cnf(c_0_7,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associativity_of_add ).
cnf(c_0_8,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_9,hypothesis,
negate(add(negate(X1),negate(add(X1,negate(X1))))) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_10,plain,
add(X1,add(X2,X3)) = add(X2,add(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_7]) ).
cnf(c_0_11,hypothesis,
add(X1,add(X1,X2)) = add(X1,X2),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_12,hypothesis,
negate(add(negate(negate(X1)),negate(add(X1,negate(X1))))) = negate(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_8]),c_0_8]) ).
cnf(c_0_13,hypothesis,
negate(add(X1,negate(add(X1,add(negate(add(X1,X2)),negate(add(X1,negate(X2)))))))) = add(negate(add(X1,X2)),negate(add(X1,negate(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_5]),c_0_7]),c_0_8]),c_0_10]) ).
cnf(c_0_14,hypothesis,
add(X1,add(X2,X1)) = add(X2,X1),
inference(spm,[status(thm)],[c_0_11,c_0_8]) ).
cnf(c_0_15,hypothesis,
negate(add(negate(X1),negate(add(X1,add(negate(X1),negate(add(X1,negate(X1)))))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_9]),c_0_7]),c_0_8]),c_0_10]) ).
cnf(c_0_16,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_17,hypothesis,
add(X1,negate(add(X1,negate(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_9]),c_0_14]),c_0_8]),c_0_10]),c_0_15]),c_0_14]),c_0_8]) ).
cnf(c_0_18,plain,
add(X1,add(X2,X3)) = add(X3,add(X2,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_8]) ).
cnf(c_0_19,plain,
negate(add(negate(add(X1,X2)),negate(add(X2,negate(X1))))) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_20,hypothesis,
add(X1,add(X2,negate(add(X1,negate(X1))))) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_21,hypothesis,
negate(add(negate(add(X1,X2)),negate(add(X1,add(negate(X2),negate(add(X2,negate(X2)))))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_9]),c_0_8]) ).
cnf(c_0_22,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
inference(fof_simplification,[status(thm)],[prove_huntingtons_axiom]) ).
cnf(c_0_23,hypothesis,
add(X1,negate(add(X2,negate(X2)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_7]),c_0_8]),c_0_21]) ).
cnf(c_0_24,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
c_0_22 ).
cnf(c_0_25,hypothesis,
negate(negate(X1)) = X1,
inference(rw,[status(thm)],[c_0_9,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(b),negate(a)))) != b,
inference(rw,[status(thm)],[c_0_24,c_0_8]) ).
cnf(c_0_27,hypothesis,
add(negate(add(X1,X2)),negate(add(X2,negate(X1)))) = negate(X2),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ROB023-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 04:23:40 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.59/0.50 % Version: 3.5.1
% 0.59/0.50 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.59/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.59/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.59/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.59/0.50 % Starting sh5l with 300s (1) cores
% 0.59/0.50 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 962860 completed with status 0
% 0.59/0.50 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.59/0.50 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.59/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.59/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.59/0.50 % No SInE strategy applied
% 0.59/0.50 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.59/0.50 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.59/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.59/0.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.59/0.50 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 0.59/0.50 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 0.59/0.50 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 0.59/0.50 % SubtermCWHack with pid 962864 completed with status 0
% 0.59/0.50 % Result found by SubtermCWHack
% 0.59/0.50 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.59/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.59/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.59/0.50 % No SInE strategy applied
% 0.59/0.50 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.59/0.50 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.59/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.59/0.50 % Preprocessing time : 0.001 s
% 0.59/0.50
% 0.59/0.50 % Proof found!
% 0.59/0.50 % SZS status Unsatisfiable
% 0.59/0.50 % SZS output start CNFRefutation
% See solution above
% 0.59/0.50 % Parsed axioms : 5
% 0.59/0.50 % Removed by relevancy pruning/SinE : 0
% 0.59/0.50 % Initial clauses : 5
% 0.59/0.50 % Removed in clause preprocessing : 0
% 0.59/0.50 % Initial clauses in saturation : 5
% 0.59/0.50 % Processed clauses : 752
% 0.59/0.50 % ...of these trivial : 346
% 0.59/0.50 % ...subsumed : 320
% 0.59/0.50 % ...remaining for further processing : 86
% 0.59/0.50 % Other redundant clauses eliminated : 0
% 0.59/0.50 % Clauses deleted for lack of memory : 0
% 0.59/0.50 % Backward-subsumed : 0
% 0.59/0.50 % Backward-rewritten : 27
% 0.59/0.50 % Generated clauses : 10431
% 0.59/0.50 % ...of the previous two non-redundant : 8056
% 0.59/0.50 % ...aggressively subsumed : 0
% 0.59/0.50 % Contextual simplify-reflections : 0
% 0.59/0.50 % Paramodulations : 10431
% 0.59/0.50 % Factorizations : 0
% 0.59/0.50 % NegExts : 0
% 0.59/0.50 % Equation resolutions : 0
% 0.59/0.50 % Disequality decompositions : 0
% 0.59/0.50 % Total rewrite steps : 17018
% 0.59/0.50 % ...of those cached : 13631
% 0.59/0.50 % Propositional unsat checks : 0
% 0.59/0.50 % Propositional check models : 0
% 0.59/0.50 % Propositional check unsatisfiable : 0
% 0.59/0.50 % Propositional clauses : 0
% 0.59/0.50 % Propositional clauses after purity: 0
% 0.59/0.50 % Propositional unsat core size : 0
% 0.59/0.50 % Propositional preprocessing time : 0.000
% 0.59/0.50 % Propositional encoding time : 0.000
% 0.59/0.50 % Propositional solver time : 0.000
% 0.59/0.50 % Success case prop preproc time : 0.000
% 0.59/0.50 % Success case prop encoding time : 0.000
% 0.59/0.50 % Success case prop solver time : 0.000
% 0.59/0.50 % Current number of processed clauses : 59
% 0.59/0.50 % Positive orientable unit clauses : 54
% 0.59/0.50 % Positive unorientable unit clauses: 5
% 0.59/0.50 % Negative unit clauses : 0
% 0.59/0.50 % Non-unit-clauses : 0
% 0.59/0.50 % Current number of unprocessed clauses: 7159
% 0.59/0.50 % ...number of literals in the above : 7159
% 0.59/0.50 % Current number of archived formulas : 0
% 0.59/0.50 % Current number of archived clauses : 27
% 0.59/0.50 % Clause-clause subsumption calls (NU) : 0
% 0.59/0.50 % Rec. Clause-clause subsumption calls : 0
% 0.59/0.50 % Non-unit clause-clause subsumptions : 0
% 0.59/0.50 % Unit Clause-clause subsumption calls : 35
% 0.59/0.50 % Rewrite failures with RHS unbound : 12
% 0.59/0.50 % BW rewrite match attempts : 1434
% 0.59/0.50 % BW rewrite match successes : 53
% 0.59/0.50 % Condensation attempts : 0
% 0.59/0.50 % Condensation successes : 0
% 0.59/0.50 % Termbank termtop insertions : 179700
% 0.59/0.50 % Search garbage collected termcells : 2
% 0.59/0.50
% 0.59/0.50 % -------------------------------------------------
% 0.59/0.50 % User time : 0.064 s
% 0.59/0.50 % System time : 0.010 s
% 0.59/0.50 % Total time : 0.075 s
% 0.59/0.50 % Maximum resident set size: 3328 pages
% 0.59/0.50
% 0.59/0.50 % -------------------------------------------------
% 0.59/0.50 % User time : 0.305 s
% 0.59/0.50 % System time : 0.039 s
% 0.59/0.50 % Total time : 0.344 s
% 0.59/0.50 % Maximum resident set size: 4864 pages
% 0.59/0.50 % E exiting
%------------------------------------------------------------------------------