%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PUZ021-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 : Fri Sep 25 02:31:52 PM UTC 2026
% Result : Unsatisfiable 7.23s 1.79s
% Output : Proof 7.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 87 ( 11 unt; 0 def)
% Number of atoms : 184 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 179 ( 82 ~; 97 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 149 ( 18 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,axiom,
( a_truth(Y,Z)
| says(X,Y)
| ~ a_truth(knave(X),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knaves_lie2) ).
fof(f7_nnf,plain,
! [X,Z,Y] :
( a_truth(Y,Z)
| says(X,Y)
| ~ a_truth(knave(X),Z) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Z,Y] :
( a_truth(Y,Z)
| says(X,Y)
| ~ a_truth(knave(X),Z) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( a_truth(X2,X1)
| says(X0,X2)
| ~ a_truth(knave(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(f8,axiom,
( a_truth(X,Z)
| ~ a_truth(and(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjunction1) ).
fof(f8_nnf,plain,
! [X,Y,Z] :
( a_truth(X,Z)
| ~ a_truth(and(X,Y),Z) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z] :
( a_truth(X,Z)
| ~ a_truth(and(X,Y),Z) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( a_truth(X0,X2)
| ~ a_truth(and(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(f12,negated_conjecture,
( a_truth(and(knave(me),rich(me)),X)
| says(me,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_statement_exists2) ).
fof(f12_nnf,plain,
! [X] :
( a_truth(and(knave(me),rich(me)),X)
| says(me,X) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X] :
( a_truth(and(knave(me),rich(me)),X)
| says(me,X) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( a_truth(and(knave(me),rich(me)),X0)
| says(me,X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p13,plain,
( says(me,X0)
| a_truth(knave(me),X0) ),
inference(resolution,[status(thm)],[c8,c12]) ).
cnf(p23,plain,
( says(me,X1)
| a_truth(X0,X1)
| says(me,X0) ),
inference(resolution,[status(thm)],[c7,p13]) ).
cnf(p24,plain,
( a_truth(X0,X0)
| says(me,X0) ),
inference(factoring,[status(thm)],[p23]) ).
cnf(p45,plain,
( a_truth(X0,and(X0,X1))
| says(me,and(X0,X1)) ),
inference(resolution,[status(thm)],[p24,c8]) ).
cnf(f9,axiom,
( a_truth(Y,Z)
| ~ a_truth(and(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjunction2) ).
fof(f9_nnf,plain,
! [X,Y,Z] :
( a_truth(Y,Z)
| ~ a_truth(and(X,Y),Z) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y,Z] :
( a_truth(Y,Z)
| ~ a_truth(and(X,Y),Z) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( a_truth(X1,X2)
| ~ a_truth(and(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p14,plain,
( says(me,X0)
| a_truth(rich(me),X0) ),
inference(resolution,[status(thm)],[c9,c12]) ).
cnf(f2,axiom,
( ~ a_truth(poor(X),Y)
| ~ a_truth(rich(X),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_rich_and_poor) ).
fof(f2_nnf,plain,
! [X,Y] :
( ~ a_truth(poor(X),Y)
| ~ a_truth(rich(X),Y) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] :
( ~ a_truth(poor(X),Y)
| ~ a_truth(rich(X),Y) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ a_truth(poor(X0),X1)
| ~ a_truth(rich(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p15,plain,
( ~ a_truth(poor(me),X0)
| says(me,X0) ),
inference(resolution,[status(thm)],[p14,c2]) ).
cnf(p124,plain,
( says(me,and(poor(me),X0))
| says(me,and(poor(me),X0)) ),
inference(resolution,[status(thm)],[p45,p15]) ).
cnf(p4020,plain,
says(me,and(poor(me),X0)),
inference(factoring,[status(thm)],[p124]) ).
cnf(f6,axiom,
( ~ a_truth(Y,Z)
| ~ says(X,Y)
| ~ a_truth(knave(X),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knaves_lie1) ).
fof(f6_nnf,plain,
! [X,Z,Y] :
( ~ a_truth(Y,Z)
| ~ says(X,Y)
| ~ a_truth(knave(X),Z) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Z,Y] :
( ~ a_truth(Y,Z)
| ~ says(X,Y)
| ~ a_truth(knave(X),Z) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ a_truth(X2,X1)
| ~ says(X0,X2)
| ~ a_truth(knave(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p17,plain,
( ~ says(X0,knave(X0))
| ~ a_truth(knave(X0),X1) ),
inference(factoring,[status(thm)],[c6]) ).
cnf(f1,axiom,
( a_truth(knave(X),Y)
| a_truth(knight(X),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knight_or_knave) ).
fof(f1_nnf,plain,
! [X,Y] :
( a_truth(knave(X),Y)
| a_truth(knight(X),Y) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( a_truth(knave(X),Y)
| a_truth(knight(X),Y) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( a_truth(knave(X0),X1)
| a_truth(knight(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p20,plain,
( a_truth(knight(X0),X1)
| ~ says(X0,knave(X0)) ),
inference(resolution,[status(thm)],[p17,c1]) ).
cnf(p55,plain,
( a_truth(knight(me),X0)
| a_truth(knave(me),knave(me)) ),
inference(resolution,[status(thm)],[p24,p20]) ).
cnf(f4,axiom,
( a_truth(Y,Z)
| ~ says(X,Y)
| ~ a_truth(knight(X),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knights_tell_truth1) ).
fof(f4_nnf,plain,
! [X,Z,Y] :
( a_truth(Y,Z)
| ~ says(X,Y)
| ~ a_truth(knight(X),Z) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Z,Y] :
( a_truth(Y,Z)
| ~ says(X,Y)
| ~ a_truth(knight(X),Z) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( a_truth(X2,X1)
| ~ says(X0,X2)
| ~ a_truth(knight(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p109,plain,
( a_truth(X0,X1)
| ~ says(me,X0)
| a_truth(knave(me),knave(me)) ),
inference(resolution,[status(thm)],[p55,c4]) ).
cnf(p425,plain,
( ~ says(me,knave(me))
| a_truth(knave(me),knave(me)) ),
inference(factoring,[status(thm)],[p109]) ).
cnf(p437,plain,
( a_truth(knave(me),knave(me))
| a_truth(knave(me),knave(me)) ),
inference(resolution,[status(thm)],[p425,p24]) ).
cnf(p474,plain,
a_truth(knave(me),knave(me)),
inference(factoring,[status(thm)],[p437]) ).
cnf(f10,axiom,
( ~ a_truth(Y,Z)
| ~ a_truth(X,Z)
| a_truth(and(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjunction3) ).
fof(f10_nnf,plain,
! [X,Y,Z] :
( ~ a_truth(Y,Z)
| ~ a_truth(X,Z)
| a_truth(and(X,Y),Z) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,Z] :
( ~ a_truth(Y,Z)
| ~ a_truth(X,Z)
| a_truth(and(X,Y),Z) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( ~ a_truth(X1,X2)
| ~ a_truth(X0,X2)
| a_truth(and(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p515,plain,
( ~ a_truth(X0,knave(me))
| a_truth(and(knave(me),X0),knave(me)) ),
inference(resolution,[status(thm)],[p474,c10]) ).
cnf(p21,plain,
( says(me,X0)
| ~ says(me,knave(me)) ),
inference(resolution,[status(thm)],[p17,p13]) ).
cnf(p54,plain,
( says(me,X0)
| a_truth(knave(me),knave(me)) ),
inference(resolution,[status(thm)],[p24,p21]) ).
cnf(p76,plain,
( ~ a_truth(X1,knave(me))
| ~ says(me,X1)
| says(me,X0) ),
inference(resolution,[status(thm)],[p54,c6]) ).
cnf(p48,plain,
( says(me,poor(me))
| says(me,poor(me)) ),
inference(resolution,[status(thm)],[p24,p15]) ).
cnf(p57,plain,
says(me,poor(me)),
inference(factoring,[status(thm)],[p48]) ).
cnf(p237,plain,
( ~ a_truth(poor(me),knave(me))
| says(me,X0) ),
inference(resolution,[status(thm)],[p76,p57]) ).
cnf(f3,axiom,
( a_truth(poor(X),Y)
| a_truth(rich(X),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rich_or_poor) ).
fof(f3_nnf,plain,
! [X,Y] :
( a_truth(poor(X),Y)
| a_truth(rich(X),Y) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( a_truth(poor(X),Y)
| a_truth(rich(X),Y) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( a_truth(poor(X0),X1)
| a_truth(rich(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p246,plain,
( a_truth(rich(me),knave(me))
| says(me,X0) ),
inference(resolution,[status(thm)],[p237,c3]) ).
cnf(p282,plain,
( a_truth(knight(me),X0)
| a_truth(rich(me),knave(me)) ),
inference(resolution,[status(thm)],[p246,p20]) ).
cnf(f0,axiom,
( ~ a_truth(knave(X),Y)
| ~ a_truth(knight(X),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_knight_and_knave) ).
fof(f0_nnf,plain,
! [X,Y] :
( ~ a_truth(knave(X),Y)
| ~ a_truth(knight(X),Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ~ a_truth(knave(X),Y)
| ~ a_truth(knight(X),Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ a_truth(knave(X0),X1)
| ~ a_truth(knight(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p286,plain,
( ~ a_truth(knave(me),X0)
| a_truth(rich(me),knave(me)) ),
inference(resolution,[status(thm)],[p282,c0]) ).
cnf(p516,plain,
a_truth(rich(me),knave(me)),
inference(resolution,[status(thm)],[p474,p286]) ).
cnf(p1216,plain,
a_truth(and(knave(me),rich(me)),knave(me)),
inference(resolution,[status(thm)],[p515,p516]) ).
cnf(p513,plain,
( ~ a_truth(X0,knave(me))
| ~ says(me,X0) ),
inference(resolution,[status(thm)],[p474,c6]) ).
cnf(p553,plain,
( a_truth(X0,X0)
| ~ a_truth(X0,knave(me)) ),
inference(resolution,[status(thm)],[p513,p24]) ).
cnf(p1228,plain,
a_truth(and(knave(me),rich(me)),and(knave(me),rich(me))),
inference(resolution,[status(thm)],[p1216,p553]) ).
cnf(p22,plain,
( a_truth(knight(X0),X2)
| a_truth(X1,X2)
| says(X0,X1) ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(f11,negated_conjecture,
( ~ a_truth(and(knave(me),rich(me)),X)
| ~ says(me,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_statement_exists1) ).
fof(f11_nnf,plain,
! [X] :
( ~ a_truth(and(knave(me),rich(me)),X)
| ~ says(me,X) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] :
( ~ a_truth(and(knave(me),rich(me)),X)
| ~ says(me,X) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ a_truth(and(knave(me),rich(me)),X0)
| ~ says(me,X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p81,plain,
( ~ a_truth(and(knave(me),rich(me)),X0)
| a_truth(knight(me),X1)
| a_truth(X0,X1) ),
inference(resolution,[status(thm)],[p22,c11]) ).
cnf(p1395,plain,
( a_truth(knight(me),X0)
| a_truth(and(knave(me),rich(me)),X0) ),
inference(resolution,[status(thm)],[p1228,p81]) ).
cnf(p58,plain,
~ a_truth(and(knave(me),rich(me)),poor(me)),
inference(resolution,[status(thm)],[p57,c11]) ).
cnf(p3733,plain,
a_truth(knight(me),poor(me)),
inference(resolution,[status(thm)],[p1395,p58]) ).
cnf(p3752,plain,
( a_truth(X0,poor(me))
| ~ says(me,X0) ),
inference(resolution,[status(thm)],[p3733,c4]) ).
cnf(p4042,plain,
a_truth(and(poor(me),X0),poor(me)),
inference(resolution,[status(thm)],[p4020,p3752]) ).
cnf(p4095,plain,
a_truth(X0,poor(me)),
inference(resolution,[status(thm)],[p4042,c9]) ).
cnf(p4102,plain,
$false,
inference(resolution,[status(thm)],[p4095,p58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ021-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 06:42:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.23/1.79 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.23/1.79 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------