%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN982-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 : Sun Sep 27 09:43:30 AM UTC 2026
% Result : Unsatisfiable 38.25s 5.95s
% Output : CNFRefutation 38.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of formulae : 59 ( 19 unt; 0 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 164 ( 90 ~; 74 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 80 ( 11 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause3,axiom,
ssBf(na),
file('theBenchmark.p',clause3) ).
cnf(c_6,plain,
ssBf(na),
inference(clausify,[status(thm)],[clause3]) ).
fof(clause30,axiom,
! [VAR_0,VAR_1] :
( ssSb(pair(VAR_0,VAR_1))
| ~ ssBf(VAR_1)
| ~ ssM(sent(VAR_0,b,pair(VAR_0,VAR_1))) ),
file('theBenchmark.p',clause30) ).
cnf(c_7,plain,
( ssSb(pair(A,B))
| ~ ssBf(B)
| ~ ssM(sent(A,b,pair(A,B))) ),
inference(clausify,[status(thm)],[clause30]) ).
fof(clause33,axiom,
! [VAR_0,VAR_1] :
( ssM(sent(b,t,triple(b,nb(VAR_1),encr(triple(VAR_0,VAR_1,tb(VAR_1)),bt))))
| ~ ssBf(VAR_1)
| ~ ssM(sent(VAR_0,b,pair(VAR_0,VAR_1))) ),
file('theBenchmark.p',clause33) ).
cnf(c_8,plain,
( ssM(sent(b,t,triple(b,nb(B),encr(triple(A,B,tb(B)),bt))))
| ~ ssBf(B)
| ~ ssM(sent(A,b,pair(A,B))) ),
inference(clausify,[status(thm)],[clause33]) ).
fof(clause37,axiom,
! [VAR_0] :
( ~ ssBk(key(VAR_0,a))
| ~ ssIk(key(VAR_0,b)) ),
file('theBenchmark.p',clause37) ).
cnf(c_9,plain,
( ~ ssBk(key(A,a))
| ~ ssIk(key(A,b)) ),
inference(clausify,[status(thm)],[clause37]) ).
fof(clause34,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ssBk(key(VAR_1,VAR_0))
| ~ ssSb(pair(VAR_0,VAR_2))
| ~ ssM(sent(VAR_0,b,pair(encr(triple(VAR_0,VAR_1,tb(VAR_2)),bt),encr(nb(VAR_2),VAR_1)))) ),
file('theBenchmark.p',clause34) ).
cnf(c_10,plain,
( ssBk(key(B,A))
| ~ ssSb(pair(A,C))
| ~ ssM(sent(A,b,pair(encr(triple(A,B,tb(C)),bt),encr(nb(C),B)))) ),
inference(clausify,[status(thm)],[clause34]) ).
fof(clause25,axiom,
! [VAR_0,VAR_1] :
( ssIk(key(VAR_0,VAR_1))
| ~ ssP(VAR_1)
| ~ ssIm(VAR_0) ),
file('theBenchmark.p',clause25) ).
cnf(c_15,plain,
( ssIk(key(A,B))
| ~ ssP(B)
| ~ ssIm(A) ),
inference(clausify,[status(thm)],[clause25]) ).
fof(clause29,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ssIm(encr(VAR_0,VAR_1))
| ~ ssP(VAR_2)
| ~ ssIk(key(VAR_1,VAR_2))
| ~ ssIm(VAR_0) ),
file('theBenchmark.p',clause29) ).
cnf(c_16,plain,
( ssIm(encr(A,B))
| ~ ssP(C)
| ~ ssIk(key(B,C))
| ~ ssIm(A) ),
inference(clausify,[status(thm)],[clause29]) ).
cnf(c_17,plain,
( ~ ssSb(pair(a,B))
| ~ ssM(sent(a,b,pair(encr(triple(a,A,tb(B)),bt),encr(nb(B),A))))
| ~ ssIk(key(A,b)) ),
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_18,plain,
( ssSb(pair(A,na))
| ~ ssM(sent(A,b,pair(A,na))) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_19,plain,
( ~ ssSb(pair(a,B))
| ~ ssM(sent(a,b,pair(encr(triple(a,A,tb(B)),bt),encr(nb(B),A))))
| ~ ssP(b)
| ~ ssIm(A) ),
inference(resolve,[status(thm)],[c_15,c_17]) ).
cnf(c_20,plain,
( ~ ssM(sent(a,b,pair(encr(triple(a,A,tb(na)),bt),encr(nb(na),A))))
| ~ ssP(b)
| ~ ssIm(A)
| ~ ssM(sent(a,b,pair(a,na))) ),
inference(resolve,[status(thm)],[c_18,c_19]) ).
fof(clause27,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ssM(sent(VAR_1,VAR_2,VAR_0))
| ~ ssP(VAR_2)
| ~ ssP(VAR_1)
| ~ ssIm(VAR_0) ),
file('theBenchmark.p',clause27) ).
cnf(c_26,plain,
( ssM(sent(B,C,A))
| ~ ssP(C)
| ~ ssP(B)
| ~ ssIm(A) ),
inference(clausify,[status(thm)],[clause27]) ).
fof(clause26,axiom,
! [VAR_0,VAR_1] :
( ssIm(pair(VAR_0,VAR_1))
| ~ ssIm(VAR_1)
| ~ ssIm(VAR_0) ),
file('theBenchmark.p',clause26) ).
cnf(c_27,plain,
( ssIm(pair(A,B))
| ~ ssIm(B)
| ~ ssIm(A) ),
inference(clausify,[status(thm)],[clause26]) ).
fof(clause20,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ssIm(VAR_2)
| ~ ssM(sent(VAR_0,VAR_1,VAR_2)) ),
file('theBenchmark.p',clause20) ).
cnf(c_32,plain,
( ssIm(C)
| ~ ssM(sent(A,B,C)) ),
inference(clausify,[status(thm)],[clause20]) ).
fof(clause18,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ssIm(VAR_1)
| ~ ssIm(triple(VAR_0,VAR_1,VAR_2)) ),
file('theBenchmark.p',clause18) ).
cnf(c_34,plain,
( ssIm(B)
| ~ ssIm(triple(A,B,C)) ),
inference(clausify,[status(thm)],[clause18]) ).
fof(clause17,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ssIm(VAR_2)
| ~ ssIm(triple(VAR_0,VAR_1,VAR_2)) ),
file('theBenchmark.p',clause17) ).
cnf(c_35,plain,
( ssIm(C)
| ~ ssIm(triple(A,B,C)) ),
inference(clausify,[status(thm)],[clause17]) ).
fof(clause16,axiom,
ssM(sent(a,b,pair(a,na))),
file('theBenchmark.p',clause16) ).
cnf(c_36,plain,
ssM(sent(a,b,pair(a,na))),
inference(clausify,[status(thm)],[clause16]) ).
fof(clause14,axiom,
! [VAR_0,VAR_1] :
( ssIm(VAR_1)
| ~ ssIm(pair(VAR_0,VAR_1)) ),
file('theBenchmark.p',clause14) ).
cnf(c_38,plain,
( ssIm(B)
| ~ ssIm(pair(A,B)) ),
inference(clausify,[status(thm)],[clause14]) ).
fof(clause5,axiom,
ssP(a),
file('theBenchmark.p',clause5) ).
cnf(c_41,plain,
ssP(a),
inference(clausify,[status(thm)],[clause5]) ).
fof(clause4,axiom,
ssP(b),
file('theBenchmark.p',clause4) ).
cnf(c_42,plain,
ssP(b),
inference(clausify,[status(thm)],[clause4]) ).
fof(clause2,axiom,
ssP(t),
file('theBenchmark.p',clause2) ).
cnf(c_43,plain,
ssP(t),
inference(clausify,[status(thm)],[clause2]) ).
cnf(c_44,plain,
( ssM(sent(b,t,triple(b,nb(na),encr(triple(A,na,tb(na)),bt))))
| ~ ssM(sent(A,b,pair(A,na))) ),
inference(resolve,[status(thm)],[c_6,c_8]) ).
cnf(c_46,plain,
( ssIm(encr(C,A))
| ~ ssP(B)
| ~ ssIm(C)
| ~ ssP(B)
| ~ ssIm(A) ),
inference(resolve,[status(thm)],[c_15,c_16]) ).
cnf(c_47,plain,
( ssIm(encr(C,A))
| ~ ssIm(C)
| ~ ssP(B)
| ~ ssIm(A) ),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_17156,plain,
( ~ ssM(sent(a,b,pair(encr(triple(a,A,tb(na)),bt),encr(nb(na),A))))
| ~ ssP(b)
| ~ ssIm(A) ),
inference(resolve,[status(thm)],[c_36,c_20]) ).
cnf(c_48,plain,
( ~ ssM(sent(a,b,pair(encr(triple(a,A,tb(na)),bt),encr(nb(na),A))))
| ~ ssIm(A) ),
inference(resolve,[status(thm)],[c_42,c_17156]) ).
cnf(c_49,plain,
ssIm(pair(a,na)),
inference(resolve,[status(thm)],[c_32,c_36]) ).
cnf(c_50,plain,
ssM(sent(b,t,triple(b,nb(na),encr(triple(a,na,tb(na)),bt)))),
inference(resolve,[status(thm)],[c_44,c_36]) ).
cnf(c_17157,plain,
( ~ ssP(b)
| ~ ssP(a)
| ~ ssIm(pair(encr(triple(a,A,tb(na)),bt),encr(nb(na),A)))
| ~ ssIm(A) ),
inference(resolve,[status(thm)],[c_48,c_26]) ).
cnf(c_17158,plain,
( ~ ssP(b)
| ~ ssIm(pair(encr(triple(a,A,tb(na)),bt),encr(nb(na),A)))
| ~ ssIm(A) ),
inference(resolve,[status(thm)],[c_41,c_17157]) ).
cnf(c_51,plain,
( ~ ssIm(pair(encr(triple(a,A,tb(na)),bt),encr(nb(na),A)))
| ~ ssIm(A) ),
inference(resolve,[status(thm)],[c_42,c_17158]) ).
cnf(c_53,plain,
ssIm(na),
inference(resolve,[status(thm)],[c_38,c_49]) ).
cnf(c_66,plain,
ssIm(triple(b,nb(na),encr(triple(a,na,tb(na)),bt))),
inference(resolve,[status(thm)],[c_32,c_50]) ).
cnf(c_84,plain,
( ~ ssIm(encr(nb(na),A))
| ~ ssIm(encr(triple(a,A,tb(na)),bt))
| ~ ssIm(A) ),
inference(resolve,[status(thm)],[c_51,c_27]) ).
cnf(c_242,plain,
( ~ ssIm(encr(nb(na),na))
| ~ ssIm(encr(triple(a,na,tb(na)),bt)) ),
inference(resolve,[status(thm)],[c_53,c_84]) ).
cnf(c_16912,plain,
ssIm(encr(triple(a,na,tb(na)),bt)),
inference(resolve,[status(thm)],[c_35,c_66]) ).
cnf(c_16913,plain,
ssIm(nb(na)),
inference(resolve,[status(thm)],[c_34,c_66]) ).
cnf(c_16915,plain,
~ ssIm(encr(nb(na),na)),
inference(resolve,[status(thm)],[c_16912,c_242]) ).
cnf(c_17159,plain,
( ~ ssIm(nb(na))
| ~ ssP(A)
| ~ ssIm(na) ),
inference(resolve,[status(thm)],[c_16915,c_47]) ).
cnf(c_17160,plain,
( ~ ssIm(nb(na))
| ~ ssP(A) ),
inference(resolve,[status(thm)],[c_53,c_17159]) ).
cnf(c_17154,plain,
~ ssP(A),
inference(resolve,[status(thm)],[c_16913,c_17160]) ).
cnf(c_17155,plain,
$false,
inference(resolve,[status(thm)],[c_17154,c_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN982-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 18:53:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1958255 was started by sandbox on n019,
% 0.10/0.37 % Sat Sep 26 18:53:18 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 38.25/5.95
% 38.25/5.95 % SZS status Unsatisfiable for theBenchmark
% 38.25/5.95
% 38.25/5.95 % Proof 1 at 3.87 (+ 1.62) seconds.
% 38.25/5.95 % Length of proof is 37.
% 38.25/5.95 % Level of proof is 10.
% 38.25/5.95 % Maximum clause weight is 39.000.
% 38.25/5.95 % Given clauses 92.
% 38.25/5.95
% 38.25/5.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------