%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV234+2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 02:54:01 PM UTC 2026
% Result : Theorem 0.65s 0.62s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 50 ( 39 unt; 0 def)
% Number of atoms : 74 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 47 ( 23 ~; 19 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 72 ( 6 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(xor_zero,axiom,
! [X1,X2,X3] : xor(X1,z) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_zero) ).
fof(xor_commutes,axiom,
! [X1,X2,X3] : xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutes) ).
fof(xor_assosciative,axiom,
! [X1,X2,X3] : xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_assosciative) ).
fof(xor_self_cancel,axiom,
! [X1,X2,X3] : xor(X1,X1) = z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_self_cancel) ).
fof(key_import_cmd,axiom,
! [X1,X2,X3] :
( ( public(enc(xor(km,imp),X1))
& public(enc(xor(X1,X2),X3))
& public(X2) )
=> public(enc(xor(km,X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_import_cmd) ).
fof(encrypt_decrypt_cancel,axiom,
! [X1,X2,X3] : enc(X1,enc(inv(X1),X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_decrypt_cancel) ).
fof(initial_knowledge9,axiom,
public(enc(xor(km,imp),xor(kek,xor(pin,data)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge9) ).
fof(co1,conjecture,
public(enc(pp,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(encrypt_data_cmd,axiom,
! [X1,X2] :
( ( public(X2)
& public(X1) )
=> public(enc(enc(inv(xor(data,km)),X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_data_cmd) ).
fof(initial_knowledge2,axiom,
public(data),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge2) ).
fof(initial_knowledge5,axiom,
public(enc(xor(kek,pin),pp)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge5) ).
fof(initial_knowledge8,axiom,
public(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge8) ).
fof(c_0_12,plain,
! [X27] : xor(X27,z) = X27,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[xor_zero])]) ).
fof(c_0_13,plain,
! [X21,X22] : xor(X21,X22) = xor(X22,X21),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[xor_commutes])]) ).
fof(c_0_14,plain,
! [X23,X24,X25] : xor(X23,xor(X24,X25)) = xor(xor(X23,X24),X25),
inference(variable_rename,[status(thm)],[xor_assosciative]) ).
fof(c_0_15,plain,
! [X26] : xor(X26,X26) = z,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[xor_self_cancel])]) ).
cnf(c_0_16,plain,
xor(X1,z) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
xor(X1,X2) = xor(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X13,X14,X15] :
( public(enc(xor(km,X14),X15))
| ~ public(enc(xor(km,imp),X13))
| ~ public(enc(xor(X13,X14),X15))
| ~ public(X14) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[key_import_cmd])])]) ).
cnf(c_0_19,plain,
xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
xor(X1,X1) = z,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
xor(z,X1) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_22,plain,
! [X19,X20] : enc(X19,enc(inv(X19),X20)) = X20,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[encrypt_decrypt_cancel])]) ).
cnf(c_0_23,plain,
( ~ public(enc(xor(km,imp),X2))
| ~ public(enc(xor(X2,X1),X3))
| ~ public(X1)
| public(enc(xor(km,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
public(enc(xor(km,imp),xor(kek,xor(pin,data)))),
inference(split_conjunct,[status(thm)],[initial_knowledge9]) ).
cnf(c_0_25,plain,
xor(X1,xor(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
enc(X1,enc(inv(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( ~ public(X1)
| ~ public(enc(xor(X3,X1),X2))
| ~ public(enc(xor(imp,km),X3))
| public(enc(xor(km,X1),X2)) ),
inference(rw,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_28,plain,
public(enc(xor(imp,km),xor(kek,xor(data,pin)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_17]),c_0_17]) ).
cnf(c_0_29,plain,
xor(X1,xor(X2,X3)) = xor(X2,xor(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_19]) ).
cnf(c_0_30,plain,
xor(X1,xor(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
fof(c_0_31,negated_conjecture,
~ public(enc(pp,a)),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_32,plain,
! [X11,X12] :
( public(enc(enc(inv(xor(data,km)),X11),X12))
| ~ public(X12)
| ~ public(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[encrypt_data_cmd])])]) ).
cnf(c_0_33,plain,
enc(inv(inv(X1)),X2) = enc(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_26]) ).
cnf(c_0_34,plain,
( ~ public(X1)
| ~ public(enc(xor(data,xor(pin,xor(kek,X1))),X2))
| public(enc(xor(km,X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_19]),c_0_19]),c_0_29]),c_0_29]) ).
cnf(c_0_35,plain,
xor(X1,xor(X2,xor(X3,X1))) = xor(X2,X3),
inference(spm,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_36,plain,
public(data),
inference(split_conjunct,[status(thm)],[initial_knowledge2]) ).
cnf(c_0_37,plain,
public(enc(xor(kek,pin),pp)),
inference(split_conjunct,[status(thm)],[initial_knowledge5]) ).
fof(c_0_38,negated_conjecture,
~ public(enc(pp,a)),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( ~ public(X2)
| ~ public(X1)
| public(enc(enc(inv(xor(data,km)),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
enc(inv(X1),enc(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_26,c_0_33]) ).
cnf(c_0_41,plain,
( ~ public(enc(xor(pin,kek),X1))
| public(enc(xor(data,km),X1)) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]),c_0_17]) ).
cnf(c_0_42,plain,
public(enc(xor(pin,kek),pp)),
inference(rw,[status(thm)],[c_0_37,c_0_17]) ).
fof(c_0_43,negated_conjecture,
~ public(enc(pp,a)),
inference(fof_nnf,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
( ~ public(X2)
| ~ public(enc(xor(data,km),X1))
| public(enc(X1,X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
public(enc(xor(data,km),pp)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
~ public(enc(pp,a)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_47,plain,
( ~ public(X1)
| public(enc(pp,X1)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,plain,
public(a),
inference(split_conjunct,[status(thm)],[initial_knowledge8]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV234+2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n009.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 08:35:13 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.54 Running first-order theorem proving
% 0.25/0.54 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
% 0.65/0.62 % Version: 3.5.1
% 0.65/0.62 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.65/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.65/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.65/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.65/0.62 % Starting sh5l with 300s (1) cores
% 0.65/0.62 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1333540 completed with status 0
% 0.65/0.62 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.65/0.62 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.65/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.65/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.65/0.62 % No SInE strategy applied
% 0.65/0.62 % Search class: FHUSM-FFSM21-MFFFFFNN
% 0.65/0.62 % partial match(1): FHUSM-FFSF21-MFFFFFNN
% 0.65/0.62 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.65/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.65/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.65/0.62 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.65/0.62 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 0.65/0.62 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.65/0.62 % G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with pid 1333550 completed with status 0
% 0.65/0.62 % Result found by G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y
% 0.65/0.62 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.65/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.65/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.65/0.62 % No SInE strategy applied
% 0.65/0.62 % Search class: FHUSM-FFSM21-MFFFFFNN
% 0.65/0.62 % partial match(1): FHUSM-FFSF21-MFFFFFNN
% 0.65/0.62 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.65/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.65/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.65/0.62 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.65/0.62 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 0.65/0.62 % Preprocessing time : 0.001 s
% 0.65/0.62 % Presaturation interreduction done
% 0.65/0.62
% 0.65/0.62 % Proof found!
% 0.65/0.62 % SZS status Theorem
% 0.65/0.62 % SZS output start CNFRefutation
% See solution above
% 0.65/0.62 % Parsed axioms : 22
% 0.65/0.62 % Removed by relevancy pruning/SinE : 0
% 0.65/0.62 % Initial clauses : 22
% 0.65/0.62 % Removed in clause preprocessing : 0
% 0.65/0.62 % Initial clauses in saturation : 22
% 0.65/0.62 % Processed clauses : 517
% 0.65/0.62 % ...of these trivial : 32
% 0.65/0.62 % ...subsumed : 349
% 0.65/0.62 % ...remaining for further processing : 136
% 0.65/0.62 % Other redundant clauses eliminated : 0
% 0.65/0.62 % Clauses deleted for lack of memory : 0
% 0.65/0.62 % Backward-subsumed : 4
% 0.65/0.62 % Backward-rewritten : 0
% 0.65/0.62 % Generated clauses : 1773
% 0.65/0.62 % ...of the previous two non-redundant : 1562
% 0.65/0.62 % ...aggressively subsumed : 0
% 0.65/0.62 % Contextual simplify-reflections : 0
% 0.65/0.62 % Paramodulations : 1773
% 0.65/0.62 % Factorizations : 0
% 0.65/0.62 % NegExts : 0
% 0.65/0.62 % Equation resolutions : 0
% 0.65/0.62 % Disequality decompositions : 0
% 0.65/0.62 % Total rewrite steps : 1042
% 0.65/0.62 % ...of those cached : 862
% 0.65/0.62 % Propositional unsat checks : 0
% 0.65/0.62 % Propositional check models : 0
% 0.65/0.62 % Propositional check unsatisfiable : 0
% 0.65/0.62 % Propositional clauses : 0
% 0.65/0.62 % Propositional clauses after purity: 0
% 0.65/0.62 % Propositional unsat core size : 0
% 0.65/0.62 % Propositional preprocessing time : 0.000
% 0.65/0.62 % Propositional encoding time : 0.000
% 0.65/0.62 % Propositional solver time : 0.000
% 0.65/0.62 % Success case prop preproc time : 0.000
% 0.65/0.62 % Success case prop encoding time : 0.000
% 0.65/0.62 % Success case prop solver time : 0.000
% 0.65/0.62 % Current number of processed clauses : 110
% 0.65/0.62 % Positive orientable unit clauses : 22
% 0.65/0.62 % Positive unorientable unit clauses: 4
% 0.65/0.62 % Negative unit clauses : 11
% 0.65/0.62 % Non-unit-clauses : 73
% 0.65/0.62 % Current number of unprocessed clauses: 1087
% 0.65/0.62 % ...number of literals in the above : 3972
% 0.65/0.62 % Current number of archived formulas : 0
% 0.65/0.62 % Current number of archived clauses : 26
% 0.65/0.62 % Clause-clause subsumption calls (NU) : 3808
% 0.65/0.62 % Rec. Clause-clause subsumption calls : 2650
% 0.65/0.62 % Non-unit clause-clause subsumptions : 273
% 0.65/0.62 % Unit Clause-clause subsumption calls : 241
% 0.65/0.62 % Rewrite failures with RHS unbound : 0
% 0.65/0.62 % BW rewrite match attempts : 51
% 0.65/0.62 % BW rewrite match successes : 38
% 0.65/0.62 % Condensation attempts : 517
% 0.65/0.62 % Condensation successes : 20
% 0.65/0.62 % Termbank termtop insertions : 28634
% 0.65/0.62 % Search garbage collected termcells : 133
% 0.65/0.62
% 0.65/0.62 % -------------------------------------------------
% 0.65/0.62 % User time : 0.035 s
% 0.65/0.62 % System time : 0.007 s
% 0.65/0.62 % Total time : 0.041 s
% 0.65/0.62 % Maximum resident set size: 3396 pages
% 0.65/0.62
% 0.65/0.62 % -------------------------------------------------
% 0.65/0.62 % User time : 0.168 s
% 0.65/0.62 % System time : 0.025 s
% 0.65/0.62 % Total time : 0.194 s
% 0.65/0.62 % Maximum resident set size: 4864 pages
% 0.65/0.62 % E exiting
%------------------------------------------------------------------------------