%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LCL162-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 01:18:37 PM UTC 2026
% Result : Unsatisfiable 3.76s 1.18s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 57 ( 57 unt; 0 nHn; 5 RR)
% Number of literals : 57 ( 56 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 100 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_6,axiom,
and_star(xor(truth,X1),X1) = falsehood,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_6) ).
cnf(and_star_commutativity,axiom,
and_star(X1,X2) = and_star(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_commutativity) ).
cnf(axiom_5,axiom,
and_star(X1,falsehood) = falsehood,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_5) ).
cnf(axiom_2,axiom,
xor(X1,falsehood) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_2) ).
cnf(xor_commutativity,axiom,
xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutativity) ).
cnf(implies_definition,axiom,
implies(X1,X2) = xor(truth,and_star(X1,xor(truth,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
cnf(and_star_associativity,axiom,
and_star(and_star(X1,X2),X3) = and_star(X1,and_star(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_associativity) ).
cnf(axiom_7,axiom,
xor(X1,xor(truth,X2)) = xor(xor(X1,truth),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_7) ).
cnf(axiom_3,axiom,
xor(X1,X1) = falsehood,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_3) ).
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/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_8) ).
cnf(axiom_4,axiom,
and_star(X1,truth) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_4) ).
cnf(prove_wajsberg_axiom,negated_conjecture,
implies(implies(x,y),implies(implies(y,z),implies(x,z))) != truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_axiom) ).
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,axiom,
and_star(X1,falsehood) = falsehood,
axiom_5 ).
cnf(c_0_15,axiom,
xor(X1,falsehood) = X1,
axiom_2 ).
cnf(c_0_16,axiom,
xor(X1,X2) = xor(X2,X1),
xor_commutativity ).
cnf(c_0_17,axiom,
implies(X1,X2) = xor(truth,and_star(X1,xor(truth,X2))),
implies_definition ).
cnf(c_0_18,axiom,
and_star(and_star(X1,X2),X3) = and_star(X1,and_star(X2,X3)),
and_star_associativity ).
cnf(c_0_19,plain,
and_star(X1,xor(truth,X1)) = falsehood,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,plain,
and_star(falsehood,X1) = falsehood,
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_21,axiom,
xor(X1,xor(truth,X2)) = xor(xor(X1,truth),X2),
axiom_7 ).
cnf(c_0_22,axiom,
xor(X1,X1) = falsehood,
axiom_3 ).
cnf(c_0_23,plain,
xor(falsehood,X1) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_24,plain,
xor(truth,and_star(xor(truth,X1),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_25,plain,
and_star(X1,and_star(xor(truth,X1),X2)) = falsehood,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_26,plain,
xor(truth,xor(truth,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_27,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_28,plain,
implies(and_star(X1,X2),X1) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_15]),c_0_26]) ).
cnf(c_0_29,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_27,c_0_16]),c_0_13]),c_0_16]),c_0_13]) ).
cnf(c_0_30,plain,
xor(truth,and_star(X1,xor(X2,truth))) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_31,plain,
xor(truth,xor(X1,truth)) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_32,plain,
implies(and_star(X1,and_star(X2,X3)),and_star(X1,X2)) = truth,
inference(spm,[status(thm)],[c_0_28,c_0_18]) ).
cnf(c_0_33,plain,
and_star(X1,implies(X1,X2)) = and_star(X2,implies(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_24]),c_0_24]) ).
cnf(c_0_34,axiom,
and_star(X1,truth) = X1,
axiom_4 ).
cnf(c_0_35,plain,
xor(truth,and_star(xor(X1,truth),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_30,c_0_13]) ).
cnf(c_0_36,plain,
implies(X1,xor(X2,truth)) = xor(truth,and_star(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_31]) ).
cnf(c_0_37,plain,
implies(and_star(X1,and_star(X2,implies(X2,X3))),and_star(X1,X3)) = truth,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
and_star(X1,and_star(X2,xor(truth,X1))) = falsehood,
inference(spm,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_39,plain,
implies(X1,and_star(X2,xor(truth,X3))) = xor(truth,and_star(X1,implies(X2,X3))),
inference(spm,[status(thm)],[c_0_17,c_0_17]) ).
cnf(c_0_40,plain,
implies(X1,falsehood) = xor(truth,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_34]) ).
cnf(c_0_41,plain,
xor(truth,and_star(X1,and_star(X2,xor(truth,X3)))) = implies(and_star(X1,X2),X3),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_42,plain,
implies(X1,and_star(X1,X2)) = implies(implies(xor(X2,truth),X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_33]),c_0_36]),c_0_17]) ).
cnf(c_0_43,plain,
implies(X1,and_star(xor(truth,X2),X3)) = xor(truth,and_star(implies(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_24,c_0_24]) ).
cnf(c_0_44,plain,
implies(X1,xor(truth,X2)) = xor(truth,and_star(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_45,plain,
xor(truth,implies(X1,X2)) = and_star(X1,xor(truth,X2)),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_46,negated_conjecture,
implies(implies(x,y),implies(implies(y,z),implies(x,z))) != truth,
inference(fof_simplification,[status(thm)],[prove_wajsberg_axiom]) ).
cnf(c_0_47,plain,
implies(and_star(X1,X2),and_star(X2,implies(X3,X1))) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40]),c_0_41]) ).
cnf(c_0_48,plain,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_17]),c_0_44]),c_0_35]) ).
cnf(c_0_49,plain,
implies(X1,implies(X2,X3)) = implies(and_star(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_45]),c_0_41]) ).
cnf(c_0_50,negated_conjecture,
implies(implies(x,y),implies(implies(y,z),implies(x,z))) != truth,
c_0_46 ).
cnf(c_0_51,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_18,c_0_13]),c_0_18]) ).
cnf(c_0_52,plain,
implies(and_star(X1,implies(X1,and_star(X2,X3))),X3) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_44]),c_0_39]),c_0_18]),c_0_24]) ).
cnf(c_0_53,plain,
and_star(implies(X1,X2),implies(implies(X2,X1),X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_48]),c_0_49]),c_0_28]),c_0_34]) ).
cnf(c_0_54,negated_conjecture,
implies(and_star(x,and_star(implies(x,y),implies(y,z))),z) != truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_49]),c_0_49]),c_0_18]),c_0_13]),c_0_51]) ).
cnf(c_0_55,plain,
implies(and_star(X1,and_star(implies(X1,X2),implies(X2,X3))),X3) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_49]),c_0_18]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL162-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 % Computer : n016.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 00:12:39 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.50 Running first-order theorem proving
% 0.16/0.50 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 3.76/1.18 % Version: 3.5.1
% 3.76/1.18 % Preprocessing class: FSSSSMSSSSSNFFN.
% 3.76/1.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.76/1.18 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 3.76/1.18 % Starting new_bool_3 with 300s (1) cores
% 3.76/1.18 % Starting new_bool_1 with 300s (1) cores
% 3.76/1.18 % Starting sh5l with 300s (1) cores
% 3.76/1.18 % new_bool_3 with pid 1153301 completed with status 0
% 3.76/1.18 % Result found by new_bool_3
% 3.76/1.18 % Preprocessing class: FSSSSMSSSSSNFFN.
% 3.76/1.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.76/1.18 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 3.76/1.18 % Starting new_bool_3 with 300s (1) cores
% 3.76/1.18 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 3.76/1.18 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.76/1.18 % Search class: FUUPM-FFSF22-MFFFFFNN
% 3.76/1.18 % Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 3.76/1.18 % Starting SubtermCWHack with 28s (1) cores
% 3.76/1.18 % SubtermCWHack with pid 1153308 completed with status 0
% 3.76/1.18 % Result found by SubtermCWHack
% 3.76/1.18 % Preprocessing class: FSSSSMSSSSSNFFN.
% 3.76/1.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.76/1.18 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 3.76/1.18 % Starting new_bool_3 with 300s (1) cores
% 3.76/1.18 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 3.76/1.18 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.76/1.18 % Search class: FUUPM-FFSF22-MFFFFFNN
% 3.76/1.18 % Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 3.76/1.18 % Starting SubtermCWHack with 28s (1) cores
% 3.76/1.18 % Preprocessing time : 0.001 s
% 3.76/1.18
% 3.76/1.18 % Proof found!
% 3.76/1.18 % SZS status Unsatisfiable
% 3.76/1.18 % SZS output start CNFRefutation
% See solution above
% 3.76/1.18 % Parsed axioms : 14
% 3.76/1.18 % Removed by relevancy pruning/SinE : 2
% 3.76/1.18 % Initial clauses : 12
% 3.76/1.18 % Removed in clause preprocessing : 0
% 3.76/1.18 % Initial clauses in saturation : 12
% 3.76/1.18 % Processed clauses : 2301
% 3.76/1.18 % ...of these trivial : 1627
% 3.76/1.18 % ...subsumed : 378
% 3.76/1.18 % ...remaining for further processing : 296
% 3.76/1.18 % Other redundant clauses eliminated : 0
% 3.76/1.18 % Clauses deleted for lack of memory : 0
% 3.76/1.18 % Backward-subsumed : 0
% 3.76/1.18 % Backward-rewritten : 12
% 3.76/1.18 % Generated clauses : 66838
% 3.76/1.18 % ...of the previous two non-redundant : 26906
% 3.76/1.18 % ...aggressively subsumed : 0
% 3.76/1.18 % Contextual simplify-reflections : 0
% 3.76/1.18 % Paramodulations : 66838
% 3.76/1.18 % Factorizations : 0
% 3.76/1.18 % NegExts : 0
% 3.76/1.18 % Equation resolutions : 0
% 3.76/1.18 % Disequality decompositions : 0
% 3.76/1.18 % Total rewrite steps : 162870
% 3.76/1.18 % ...of those cached : 130922
% 3.76/1.18 % Propositional unsat checks : 0
% 3.76/1.18 % Propositional check models : 0
% 3.76/1.18 % Propositional check unsatisfiable : 0
% 3.76/1.18 % Propositional clauses : 0
% 3.76/1.18 % Propositional clauses after purity: 0
% 3.76/1.18 % Propositional unsat core size : 0
% 3.76/1.18 % Propositional preprocessing time : 0.000
% 3.76/1.18 % Propositional encoding time : 0.000
% 3.76/1.18 % Propositional solver time : 0.000
% 3.76/1.18 % Success case prop preproc time : 0.000
% 3.76/1.18 % Success case prop encoding time : 0.000
% 3.76/1.18 % Success case prop solver time : 0.000
% 3.76/1.18 % Current number of processed clauses : 284
% 3.76/1.18 % Positive orientable unit clauses : 262
% 3.76/1.18 % Positive unorientable unit clauses: 22
% 3.76/1.18 % Negative unit clauses : 0
% 3.76/1.18 % Non-unit-clauses : 0
% 3.76/1.18 % Current number of unprocessed clauses: 24493
% 3.76/1.18 % ...number of literals in the above : 24493
% 3.76/1.18 % Current number of archived formulas : 0
% 3.76/1.18 % Current number of archived clauses : 12
% 3.76/1.18 % Clause-clause subsumption calls (NU) : 0
% 3.76/1.18 % Rec. Clause-clause subsumption calls : 0
% 3.76/1.18 % Non-unit clause-clause subsumptions : 0
% 3.76/1.18 % Unit Clause-clause subsumption calls : 71
% 3.76/1.18 % Rewrite failures with RHS unbound : 0
% 3.76/1.18 % BW rewrite match attempts : 4232
% 3.76/1.18 % BW rewrite match successes : 156
% 3.76/1.18 % Condensation attempts : 0
% 3.76/1.18 % Condensation successes : 0
% 3.76/1.18 % Termbank termtop insertions : 766138
% 3.76/1.18 % Search garbage collected termcells : 6
% 3.76/1.18
% 3.76/1.18 % -------------------------------------------------
% 3.76/1.18 % User time : 0.574 s
% 3.76/1.18 % System time : 0.032 s
% 3.76/1.18 % Total time : 0.606 s
% 3.76/1.18 % Maximum resident set size: 3588 pages
% 3.76/1.18
% 3.76/1.18 % -------------------------------------------------
% 3.76/1.18 % User time : 0.577 s
% 3.76/1.18 % System time : 0.038 s
% 3.76/1.18 % Total time : 0.615 s
% 3.76/1.18 % Maximum resident set size: 4864 pages
% 3.76/1.18 % E exiting
%------------------------------------------------------------------------------