%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO029-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:07:01 PM UTC 2026
% Result : Unsatisfiable 0.25s 0.57s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 4 RR)
% Number of literals : 28 ( 27 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(l1,axiom,
add(X1,multiply(X2,multiply(X1,X3))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
cnf(l2,axiom,
multiply(X1,add(X2,add(X1,X3))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2) ).
cnf(associativity_of_add,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).
cnf(b1,axiom,
multiply(add(X1,X2),add(X1,inverse(X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b1) ).
cnf(b2,axiom,
add(multiply(X1,X2),multiply(X1,inverse(X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(prove_equal_inverse,negated_conjecture,
add(b,inverse(b)) != add(a,inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equal_inverse) ).
cnf(c_0_8,axiom,
add(X1,multiply(X2,multiply(X1,X3))) = X1,
l1 ).
cnf(c_0_9,axiom,
multiply(X1,add(X2,add(X1,X3))) = X1,
l2 ).
cnf(c_0_10,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associativity_of_add ).
cnf(c_0_11,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,axiom,
multiply(add(X1,X2),add(X1,inverse(X2))) = X1,
b1 ).
cnf(c_0_13,plain,
add(X1,add(multiply(X2,X1),X3)) = add(X1,X3),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,axiom,
add(multiply(X1,X2),multiply(X1,inverse(X2))) = X1,
b2 ).
cnf(c_0_15,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_16,plain,
add(X1,add(X2,multiply(X3,X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_12]),c_0_10]) ).
cnf(c_0_17,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
add(X1,add(X2,X3)) = add(X2,add(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_15]),c_0_10]) ).
cnf(c_0_19,plain,
multiply(X1,add(X2,add(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_20,plain,
add(X1,add(inverse(X1),X2)) = add(X1,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_15]) ).
cnf(c_0_21,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_22,plain,
multiply(X1,add(X2,inverse(X2))) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
add(b,inverse(b)) != add(a,inverse(a)),
inference(fof_simplification,[status(thm)],[prove_equal_inverse]) ).
cnf(c_0_24,plain,
multiply(add(X1,inverse(X1)),X2) = X2,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
add(b,inverse(b)) != add(a,inverse(a)),
c_0_23 ).
cnf(c_0_26,plain,
add(X1,inverse(X1)) = add(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_24]),c_0_24]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_25,c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO029-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.46 % Computer : n009.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Mon Sep 21 13:49:12 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.53 Running first-order theorem proving
% 0.25/0.53 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
% 0.25/0.57 % Version: 3.5.1
% 0.25/0.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.57 % Starting sh5l with 300s (1) cores
% 0.25/0.57 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1918488 completed with status 0
% 0.25/0.57 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.25/0.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.57 % No SInE strategy applied
% 0.25/0.57 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.25/0.57 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.25/0.57 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 0.25/0.57 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 0.25/0.57 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 0.25/0.57 % G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with pid 1918498 completed with status 0
% 0.25/0.57 % Result found by G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y
% 0.25/0.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.57 % No SInE strategy applied
% 0.25/0.57 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.25/0.57 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.25/0.57 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 0.25/0.57 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 0.25/0.57 % Preprocessing time : 0.002 s
% 0.25/0.57
% 0.25/0.57 % Proof found!
% 0.25/0.57 % SZS status Unsatisfiable
% 0.25/0.57 % SZS output start CNFRefutation
% See solution above
% 0.25/0.57 % Parsed axioms : 11
% 0.25/0.57 % Removed by relevancy pruning/SinE : 0
% 0.25/0.57 % Initial clauses : 11
% 0.25/0.57 % Removed in clause preprocessing : 0
% 0.25/0.57 % Initial clauses in saturation : 11
% 0.25/0.57 % Processed clauses : 79
% 0.25/0.57 % ...of these trivial : 27
% 0.25/0.57 % ...subsumed : 18
% 0.25/0.57 % ...remaining for further processing : 34
% 0.25/0.57 % Other redundant clauses eliminated : 0
% 0.25/0.57 % Clauses deleted for lack of memory : 0
% 0.25/0.57 % Backward-subsumed : 0
% 0.25/0.57 % Backward-rewritten : 2
% 0.25/0.57 % Generated clauses : 650
% 0.25/0.57 % ...of the previous two non-redundant : 406
% 0.25/0.57 % ...aggressively subsumed : 0
% 0.25/0.57 % Contextual simplify-reflections : 0
% 0.25/0.57 % Paramodulations : 649
% 0.25/0.57 % Factorizations : 0
% 0.25/0.57 % NegExts : 0
% 0.25/0.57 % Equation resolutions : 0
% 0.25/0.57 % Disequality decompositions : 0
% 0.25/0.57 % Total rewrite steps : 521
% 0.25/0.57 % ...of those cached : 309
% 0.25/0.57 % Propositional unsat checks : 0
% 0.25/0.57 % Propositional check models : 0
% 0.25/0.57 % Propositional check unsatisfiable : 0
% 0.25/0.57 % Propositional clauses : 0
% 0.25/0.57 % Propositional clauses after purity: 0
% 0.25/0.57 % Propositional unsat core size : 0
% 0.25/0.57 % Propositional preprocessing time : 0.000
% 0.25/0.57 % Propositional encoding time : 0.000
% 0.25/0.57 % Propositional solver time : 0.000
% 0.25/0.57 % Success case prop preproc time : 0.000
% 0.25/0.57 % Success case prop encoding time : 0.000
% 0.25/0.57 % Success case prop solver time : 0.000
% 0.25/0.57 % Current number of processed clauses : 31
% 0.25/0.57 % Positive orientable unit clauses : 26
% 0.25/0.57 % Positive unorientable unit clauses: 5
% 0.25/0.57 % Negative unit clauses : 0
% 0.25/0.57 % Non-unit-clauses : 0
% 0.25/0.57 % Current number of unprocessed clauses: 327
% 0.25/0.57 % ...number of literals in the above : 327
% 0.25/0.57 % Current number of archived formulas : 0
% 0.25/0.57 % Current number of archived clauses : 3
% 0.25/0.57 % Clause-clause subsumption calls (NU) : 0
% 0.25/0.57 % Rec. Clause-clause subsumption calls : 0
% 0.25/0.57 % Non-unit clause-clause subsumptions : 0
% 0.25/0.57 % Unit Clause-clause subsumption calls : 4
% 0.25/0.57 % Rewrite failures with RHS unbound : 16
% 0.25/0.57 % BW rewrite match attempts : 86
% 0.25/0.57 % BW rewrite match successes : 32
% 0.25/0.57 % Condensation attempts : 79
% 0.25/0.57 % Condensation successes : 0
% 0.25/0.57 % Termbank termtop insertions : 3804
% 0.25/0.57 % Search garbage collected termcells : 2
% 0.25/0.57
% 0.25/0.57 % -------------------------------------------------
% 0.25/0.57 % User time : 0.014 s
% 0.25/0.57 % System time : 0.002 s
% 0.25/0.57 % Total time : 0.016 s
% 0.25/0.57 % Maximum resident set size: 3636 pages
% 0.25/0.57
% 0.25/0.57 % -------------------------------------------------
% 0.25/0.57 % User time : 0.065 s
% 0.25/0.57 % System time : 0.019 s
% 0.25/0.57 % Total time : 0.084 s
% 0.25/0.57 % Maximum resident set size: 4864 pages
% 0.25/0.57 % E exiting
%------------------------------------------------------------------------------