%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL109-6 : 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 : n008.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 01:11:47 PM UTC 2026
% Result : Unsatisfiable 8.47s 1.70s
% Output : CNFRefutation 8.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 7 RR)
% Number of literals : 47 ( 46 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_6,axiom,
and_star(xor(truth,X1),X1) = falsehood,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_6) ).
cnf(and_star_commutativity,axiom,
and_star(X1,X2) = and_star(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_commutativity) ).
cnf(xor_commutativity,axiom,
xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutativity) ).
cnf(axiom_5,axiom,
and_star(X1,falsehood) = falsehood,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_5) ).
cnf(axiom_2,axiom,
xor(X1,falsehood) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_2) ).
cnf(axiom_8,axiom,
and_star(xor(and_star(xor(truth,X1),X2),truth),X2) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_8) ).
cnf(and_star_associativity,axiom,
and_star(and_star(X1,X2),X3) = and_star(X1,and_star(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_associativity) ).
cnf(axiom_7,axiom,
xor(X1,xor(truth,X2)) = xor(xor(X1,truth),X2),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_7) ).
cnf(axiom_3,axiom,
xor(X1,X1) = falsehood,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_3) ).
cnf(axiom_4,axiom,
and_star(X1,truth) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-0.ax',axiom_4) ).
cnf(prove_wajsberg_mv_4,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_mv_4) ).
cnf(implies_definition,axiom,
implies(X1,X2) = xor(truth,and_star(X1,xor(truth,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
cnf(c_0_12,axiom,
and_star(xor(truth,X1),X1) = falsehood,
axiom_6 ).
cnf(c_0_13,axiom,
and_star(X1,X2) = and_star(X2,X1),
and_star_commutativity ).
cnf(c_0_14,plain,
and_star(X1,xor(truth,X1)) = falsehood,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
xor(X1,X2) = xor(X2,X1),
xor_commutativity ).
cnf(c_0_16,axiom,
and_star(X1,falsehood) = falsehood,
axiom_5 ).
cnf(c_0_17,axiom,
xor(X1,falsehood) = X1,
axiom_2 ).
cnf(c_0_18,axiom,
and_star(xor(and_star(xor(truth,X1),X2),truth),X2) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1),
axiom_8 ).
cnf(c_0_19,axiom,
and_star(and_star(X1,X2),X3) = and_star(X1,and_star(X2,X3)),
and_star_associativity ).
cnf(c_0_20,plain,
and_star(X1,xor(X1,truth)) = falsehood,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
and_star(falsehood,X1) = falsehood,
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_22,axiom,
xor(X1,xor(truth,X2)) = xor(xor(X1,truth),X2),
axiom_7 ).
cnf(c_0_23,axiom,
xor(X1,X1) = falsehood,
axiom_3 ).
cnf(c_0_24,plain,
xor(falsehood,X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_25,plain,
and_star(X1,xor(truth,and_star(xor(truth,X2),X1))) = and_star(X2,xor(truth,and_star(xor(truth,X1),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_15]),c_0_13]),c_0_15]),c_0_13]) ).
cnf(c_0_26,plain,
and_star(X1,and_star(xor(X1,truth),X2)) = falsehood,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_27,plain,
xor(truth,xor(truth,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_28,axiom,
and_star(X1,truth) = X1,
axiom_4 ).
cnf(c_0_29,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
inference(fof_simplification,[status(thm)],[prove_wajsberg_mv_4]) ).
cnf(c_0_30,plain,
and_star(X1,and_star(X2,X3)) = and_star(X2,and_star(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_13]),c_0_19]) ).
cnf(c_0_31,plain,
and_star(X1,xor(truth,and_star(X1,xor(truth,and_star(X1,X2))))) = and_star(X1,X2),
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_15]),c_0_27]),c_0_15]),c_0_27]),c_0_17]),c_0_28]),c_0_13]) ).
cnf(c_0_32,plain,
and_star(X1,xor(truth,and_star(xor(truth,X2),X1))) = and_star(X2,xor(truth,and_star(X2,xor(truth,X1)))),
inference(spm,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_33,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
c_0_29 ).
cnf(c_0_34,axiom,
implies(X1,X2) = xor(truth,and_star(X1,xor(truth,X2))),
implies_definition ).
cnf(c_0_35,plain,
and_star(X1,and_star(X2,xor(truth,and_star(xor(truth,X3),X1)))) = and_star(X2,and_star(X3,xor(truth,and_star(xor(truth,X1),X3)))),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_36,plain,
and_star(X1,xor(truth,and_star(X2,xor(truth,and_star(xor(truth,X1),X2))))) = and_star(X1,xor(truth,X2)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
xor(truth,and_star(xor(truth,and_star(xor(truth,and_star(a,xor(truth,b))),xor(truth,xor(truth,and_star(b,xor(truth,a)))))),xor(truth,xor(truth,and_star(b,xor(truth,a)))))) != truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_34]),c_0_34]),c_0_34]),c_0_34]) ).
cnf(c_0_38,plain,
and_star(X1,and_star(X2,xor(truth,and_star(xor(truth,X1),xor(truth,X2))))) = and_star(X1,X2),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_27]),c_0_27]),c_0_19]),c_0_13]),c_0_14]),c_0_16]),c_0_17]),c_0_28]),c_0_13]),c_0_19]) ).
cnf(c_0_39,negated_conjecture,
xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,xor(truth,xor(truth,and_star(b,xor(truth,a))))))))))) != truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_13]),c_0_25]),c_0_13]),c_0_19]),c_0_19]) ).
cnf(c_0_40,plain,
and_star(X1,and_star(X2,xor(truth,and_star(xor(truth,X2),xor(truth,X1))))) = and_star(X2,X1),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_41,plain,
xor(X1,xor(truth,X2)) = xor(X2,xor(X1,truth)),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_42,plain,
and_star(X1,and_star(X2,xor(truth,and_star(X1,X2)))) = falsehood,
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_43,negated_conjecture,
xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,and_star(b,xor(truth,a))))))))) != truth,
inference(spm,[status(thm)],[c_0_39,c_0_27]) ).
cnf(c_0_44,plain,
and_star(X1,and_star(xor(truth,X2),xor(truth,and_star(X2,xor(truth,X1))))) = and_star(xor(truth,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_23]),c_0_17]) ).
cnf(c_0_45,plain,
and_star(X1,and_star(X2,xor(truth,and_star(X2,X1)))) = falsehood,
inference(spm,[status(thm)],[c_0_30,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL109-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.43 % Computer : n008.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Mon Sep 21 00:06:11 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.50 Running first-order theorem proving
% 0.19/0.50 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
% 8.47/1.70 % Version: 3.5.1
% 8.47/1.70 % Preprocessing class: FSSSSMSSSSSNFFN.
% 8.47/1.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.47/1.70 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 8.47/1.70 % Starting new_bool_3 with 300s (1) cores
% 8.47/1.70 % Starting new_bool_1 with 300s (1) cores
% 8.47/1.70 % Starting sh5l with 300s (1) cores
% 8.47/1.70 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3927964 completed with status 0
% 8.47/1.70 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 8.47/1.70 % Preprocessing class: FSSSSMSSSSSNFFN.
% 8.47/1.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.47/1.70 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 8.47/1.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.47/1.70 % No SInE strategy applied
% 8.47/1.70 % Search class: FUUPM-FFSF22-DFFFFFNN
% 8.47/1.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.47/1.70 % Starting SubtermCWHack with 136s (1) cores
% 8.47/1.70 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 8.47/1.70 % Starting new_bool_3 with 370s (1) cores
% 8.47/1.70 % Starting new_bool_1 with 366s (1) cores
% 8.47/1.70 % Starting G-E--_303_C18_F1_URBAN_S0Y with 140s (1) cores
% 8.47/1.70 % new_bool_1 with pid 3927974 completed with status 0
% 8.47/1.70 % Result found by new_bool_1
% 8.47/1.70 % Preprocessing class: FSSSSMSSSSSNFFN.
% 8.47/1.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.47/1.70 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 8.47/1.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.47/1.70 % No SInE strategy applied
% 8.47/1.70 % Search class: FUUPM-FFSF22-DFFFFFNN
% 8.47/1.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.47/1.70 % Starting SubtermCWHack with 136s (1) cores
% 8.47/1.70 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 8.47/1.70 % Starting new_bool_3 with 370s (1) cores
% 8.47/1.70 % Starting new_bool_1 with 366s (1) cores
% 8.47/1.70 % Preprocessing time : 0.002 s
% 8.47/1.70 % Presaturation interreduction done
% 8.47/1.70
% 8.47/1.70 % Proof found!
% 8.47/1.70 % SZS status Unsatisfiable
% 8.47/1.70 % SZS output start CNFRefutation
% See solution above
% 8.47/1.70 % Parsed axioms : 14
% 8.47/1.70 % Removed by relevancy pruning/SinE : 0
% 8.47/1.70 % Initial clauses : 14
% 8.47/1.70 % Removed in clause preprocessing : 2
% 8.47/1.70 % Initial clauses in saturation : 12
% 8.47/1.70 % Processed clauses : 1259
% 8.47/1.70 % ...of these trivial : 804
% 8.47/1.70 % ...subsumed : 313
% 8.47/1.70 % ...remaining for further processing : 142
% 8.47/1.70 % Other redundant clauses eliminated : 0
% 8.47/1.70 % Clauses deleted for lack of memory : 0
% 8.47/1.70 % Backward-subsumed : 0
% 8.47/1.70 % Backward-rewritten : 3
% 8.47/1.70 % Generated clauses : 35154
% 8.47/1.70 % ...of the previous two non-redundant : 23743
% 8.47/1.70 % ...aggressively subsumed : 0
% 8.47/1.70 % Contextual simplify-reflections : 0
% 8.47/1.70 % Paramodulations : 35154
% 8.47/1.70 % Factorizations : 0
% 8.47/1.70 % NegExts : 0
% 8.47/1.70 % Equation resolutions : 0
% 8.47/1.70 % Disequality decompositions : 0
% 8.47/1.70 % Total rewrite steps : 108322
% 8.47/1.70 % ...of those cached : 94283
% 8.47/1.70 % Propositional unsat checks : 0
% 8.47/1.70 % Propositional check models : 0
% 8.47/1.70 % Propositional check unsatisfiable : 0
% 8.47/1.70 % Propositional clauses : 0
% 8.47/1.70 % Propositional clauses after purity: 0
% 8.47/1.70 % Propositional unsat core size : 0
% 8.47/1.70 % Propositional preprocessing time : 0.000
% 8.47/1.70 % Propositional encoding time : 0.000
% 8.47/1.70 % Propositional solver time : 0.000
% 8.47/1.70 % Success case prop preproc time : 0.000
% 8.47/1.70 % Success case prop encoding time : 0.000
% 8.47/1.70 % Success case prop solver time : 0.000
% 8.47/1.70 % Current number of processed clauses : 128
% 8.47/1.70 % Positive orientable unit clauses : 93
% 8.47/1.70 % Positive unorientable unit clauses: 33
% 8.47/1.70 % Negative unit clauses : 2
% 8.47/1.70 % Non-unit-clauses : 0
% 8.47/1.70 % Current number of unprocessed clauses: 22507
% 8.47/1.70 % ...number of literals in the above : 22507
% 8.47/1.70 % Current number of archived formulas : 0
% 8.47/1.70 % Current number of archived clauses : 16
% 8.47/1.70 % Clause-clause subsumption calls (NU) : 0
% 8.47/1.70 % Rec. Clause-clause subsumption calls : 0
% 8.47/1.70 % Non-unit clause-clause subsumptions : 0
% 8.47/1.70 % Unit Clause-clause subsumption calls : 115
% 8.47/1.70 % Rewrite failures with RHS unbound : 0
% 8.47/1.70 % BW rewrite match attempts : 2758
% 8.47/1.70 % BW rewrite match successes : 136
% 8.47/1.70 % Condensation attempts : 0
% 8.47/1.70 % Condensation successes : 0
% 8.47/1.70 % Termbank termtop insertions : 1006029
% 8.47/1.70 % Search garbage collected termcells : 2
% 8.47/1.70
% 8.47/1.70 % -------------------------------------------------
% 8.47/1.70 % User time : 1.048 s
% 8.47/1.70 % System time : 0.058 s
% 8.47/1.70 % Total time : 1.105 s
% 8.47/1.70 % Maximum resident set size: 3640 pages
% 8.47/1.70
% 8.47/1.70 % -------------------------------------------------
% 8.47/1.70 % User time : 5.095 s
% 8.47/1.70 % System time : 0.254 s
% 8.47/1.70 % Total time : 5.349 s
% 8.47/1.70 % Maximum resident set size: 4608 pages
% 8.47/1.70 % E exiting
%------------------------------------------------------------------------------