%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL159-1 : 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 : n010.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 01:11:55 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 54 ( 54 unt; 0 nHn; 10 RR)
% Number of literals : 54 ( 53 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_4,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).
cnf(wajsberg_1,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
cnf(false_definition,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',false_definition) ).
cnf(or_commutativity,axiom,
or(X1,X2) = or(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',or_commutativity) ).
cnf(or_definition,axiom,
or(X1,X2) = implies(not(X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',or_definition) ).
cnf(wajsberg_3,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
cnf(and_star_definition,axiom,
and_star(X1,X2) = not(or(not(X1),not(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',and_star_definition) ).
cnf(and_star_commutativity,axiom,
and_star(X1,X2) = and_star(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',and_star_commutativity) ).
cnf(and_definition,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',and_definition) ).
cnf(xor_definition,axiom,
xor(X1,X2) = or(and(X1,not(X2)),and(not(X1),X2)),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',xor_definition) ).
cnf(prove_alternative_wajsberg_axiom,negated_conjecture,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(xor_commutativity,axiom,
xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',xor_commutativity) ).
cnf(c_0_12,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
wajsberg_4 ).
cnf(c_0_13,axiom,
implies(truth,X1) = X1,
wajsberg_1 ).
cnf(c_0_14,axiom,
not(truth) = falsehood,
false_definition ).
cnf(c_0_15,axiom,
or(X1,X2) = or(X2,X1),
or_commutativity ).
cnf(c_0_16,axiom,
or(X1,X2) = implies(not(X1),X2),
or_definition ).
cnf(c_0_17,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
wajsberg_3 ).
cnf(c_0_18,plain,
implies(implies(not(X1),falsehood),X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_19,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).
cnf(c_0_20,plain,
implies(implies(X1,truth),truth) = implies(X1,X1),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_21,plain,
implies(implies(not(falsehood),X1),X1) = truth,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
implies(not(falsehood),not(falsehood)) = truth,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
not(falsehood) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_13]) ).
cnf(c_0_24,axiom,
and_star(X1,X2) = not(or(not(X1),not(X2))),
and_star_definition ).
cnf(c_0_25,plain,
implies(implies(not(not(X1)),X2),implies(X1,X2)) = truth,
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_26,plain,
implies(X1,X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_23]),c_0_13]) ).
cnf(c_0_27,axiom,
and_star(X1,X2) = and_star(X2,X1),
and_star_commutativity ).
cnf(c_0_28,plain,
and_star(X1,X2) = not(implies(not(not(X1)),not(X2))),
inference(rw,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_29,plain,
implies(X1,not(not(X1))) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_13]) ).
cnf(c_0_30,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
and_definition ).
cnf(c_0_31,plain,
not(implies(not(not(X1)),not(X2))) = not(implies(not(not(X2)),not(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_28]) ).
cnf(c_0_32,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_29]),c_0_13]),c_0_19]),c_0_26]),c_0_13]) ).
cnf(c_0_33,axiom,
xor(X1,X2) = or(and(X1,not(X2)),and(not(X1),X2)),
xor_definition ).
cnf(c_0_34,plain,
and(X1,X2) = not(implies(not(not(X1)),not(X2))),
inference(rw,[status(thm)],[c_0_30,c_0_16]) ).
cnf(c_0_35,plain,
implies(not(X1),truth) = implies(falsehood,X1),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_36,plain,
implies(not(X1),falsehood) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_23]),c_0_13]) ).
cnf(c_0_37,plain,
not(implies(X1,not(X2))) = not(implies(X2,not(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]) ).
cnf(c_0_38,negated_conjecture,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
inference(fof_simplification,[status(thm)],[prove_alternative_wajsberg_axiom]) ).
cnf(c_0_39,plain,
xor(X1,X2) = implies(not(not(implies(not(not(X1)),not(not(X2))))),not(implies(not(not(not(X1))),not(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_16]),c_0_34]),c_0_34]) ).
cnf(c_0_40,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_19,c_0_32]) ).
cnf(c_0_41,plain,
implies(falsehood,not(X1)) = implies(X1,truth),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_42,plain,
implies(X1,falsehood) = not(X1),
inference(spm,[status(thm)],[c_0_36,c_0_32]) ).
cnf(c_0_43,plain,
implies(X1,not(X2)) = implies(X2,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_37]),c_0_32]) ).
cnf(c_0_44,negated_conjecture,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
c_0_38 ).
cnf(c_0_45,axiom,
xor(X1,X2) = xor(X2,X1),
xor_commutativity ).
cnf(c_0_46,plain,
implies(implies(X1,X2),not(implies(X2,X1))) = xor(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_40]) ).
cnf(c_0_47,plain,
implies(X1,not(implies(X1,truth))) = not(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_41]),c_0_42]),c_0_32]),c_0_42]),c_0_43]) ).
cnf(c_0_48,negated_conjecture,
xor(y,xor(truth,x)) != xor(x,xor(truth,y)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_45]) ).
cnf(c_0_49,plain,
xor(truth,X1) = not(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_13]),c_0_47]) ).
cnf(c_0_50,plain,
xor(not(X1),not(X2)) = xor(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_40]),c_0_40]),c_0_46]) ).
cnf(c_0_51,negated_conjecture,
xor(y,not(x)) != xor(x,not(y)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49]),c_0_49]) ).
cnf(c_0_52,plain,
xor(X1,not(X2)) = xor(X2,not(X1)),
inference(spm,[status(thm)],[c_0_50,c_0_32]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 00:07:39 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.43 % Version: 3.5.1
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.43 % Starting sh5l with 300s (1) cores
% 0.12/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3838074 completed with status 0
% 0.12/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.43 % No SInE strategy applied
% 0.12/0.43 % Search class: FUUPM-FFSF21-DFFFFFNN
% 0.12/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.43 % Starting G-E--_201_C45_F1_AE_CS_SP_PI_S0Y with 136s (1) cores
% 0.12/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.12/0.43 % SubtermCWHack with pid 3838078 completed with status 0
% 0.12/0.43 % Result found by SubtermCWHack
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.43 % No SInE strategy applied
% 0.12/0.43 % Search class: FUUPM-FFSF21-DFFFFFNN
% 0.12/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.43 % Preprocessing time : 0.001 s
% 0.12/0.43
% 0.12/0.43 % Proof found!
% 0.12/0.43 % SZS status Unsatisfiable
% 0.12/0.43 % SZS output start CNFRefutation
% See solution above
% 0.12/0.43 % Parsed axioms : 17
% 0.12/0.43 % Removed by relevancy pruning/SinE : 0
% 0.12/0.43 % Initial clauses : 17
% 0.12/0.43 % Removed in clause preprocessing : 3
% 0.12/0.43 % Initial clauses in saturation : 14
% 0.12/0.43 % Processed clauses : 123
% 0.12/0.43 % ...of these trivial : 53
% 0.12/0.43 % ...subsumed : 11
% 0.12/0.43 % ...remaining for further processing : 59
% 0.12/0.43 % Other redundant clauses eliminated : 0
% 0.12/0.43 % Clauses deleted for lack of memory : 0
% 0.12/0.43 % Backward-subsumed : 1
% 0.12/0.43 % Backward-rewritten : 24
% 0.12/0.43 % Generated clauses : 1074
% 0.12/0.43 % ...of the previous two non-redundant : 585
% 0.12/0.43 % ...aggressively subsumed : 0
% 0.12/0.43 % Contextual simplify-reflections : 0
% 0.12/0.43 % Paramodulations : 1074
% 0.12/0.43 % Factorizations : 0
% 0.12/0.43 % NegExts : 0
% 0.12/0.43 % Equation resolutions : 0
% 0.12/0.43 % Disequality decompositions : 0
% 0.12/0.43 % Total rewrite steps : 1593
% 0.12/0.43 % ...of those cached : 1324
% 0.12/0.43 % Propositional unsat checks : 0
% 0.12/0.43 % Propositional check models : 0
% 0.12/0.43 % Propositional check unsatisfiable : 0
% 0.12/0.43 % Propositional clauses : 0
% 0.12/0.43 % Propositional clauses after purity: 0
% 0.12/0.43 % Propositional unsat core size : 0
% 0.12/0.43 % Propositional preprocessing time : 0.000
% 0.12/0.43 % Propositional encoding time : 0.000
% 0.12/0.43 % Propositional solver time : 0.000
% 0.12/0.43 % Success case prop preproc time : 0.000
% 0.12/0.43 % Success case prop encoding time : 0.000
% 0.12/0.43 % Success case prop solver time : 0.000
% 0.12/0.43 % Current number of processed clauses : 34
% 0.12/0.43 % Positive orientable unit clauses : 26
% 0.12/0.43 % Positive unorientable unit clauses: 8
% 0.12/0.43 % Negative unit clauses : 0
% 0.12/0.43 % Non-unit-clauses : 0
% 0.12/0.43 % Current number of unprocessed clauses: 450
% 0.12/0.43 % ...number of literals in the above : 450
% 0.12/0.43 % Current number of archived formulas : 0
% 0.12/0.43 % Current number of archived clauses : 28
% 0.12/0.43 % Clause-clause subsumption calls (NU) : 0
% 0.12/0.43 % Rec. Clause-clause subsumption calls : 0
% 0.12/0.43 % Non-unit clause-clause subsumptions : 0
% 0.12/0.43 % Unit Clause-clause subsumption calls : 12
% 0.12/0.43 % Rewrite failures with RHS unbound : 0
% 0.12/0.43 % BW rewrite match attempts : 94
% 0.12/0.43 % BW rewrite match successes : 40
% 0.12/0.43 % Condensation attempts : 0
% 0.12/0.43 % Condensation successes : 0
% 0.12/0.43 % Termbank termtop insertions : 10280
% 0.12/0.43 % Search garbage collected termcells : 2
% 0.12/0.43
% 0.12/0.43 % -------------------------------------------------
% 0.12/0.43 % User time : 0.012 s
% 0.12/0.43 % System time : 0.003 s
% 0.12/0.43 % Total time : 0.015 s
% 0.12/0.43 % Maximum resident set size: 3644 pages
% 0.12/0.43
% 0.12/0.43 % -------------------------------------------------
% 0.12/0.43 % User time : 0.063 s
% 0.12/0.43 % System time : 0.016 s
% 0.12/0.43 % Total time : 0.080 s
% 0.12/0.43 % Maximum resident set size: 4608 pages
% 0.12/0.43 % E exiting
%------------------------------------------------------------------------------