%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PUZ026-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:31:53 PM UTC 2026
% Result : Unsatisfiable 2.36s 0.77s
% Output : Proof 2.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 86 ( 16 unt; 0 def)
% Number of atoms : 217 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 232 ( 101 ~; 131 |; 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; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 99 ( 26 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
( a_truth(normal(Y))
| a_truth(truthteller(Y))
| ~ a_truth(says(Y,X))
| ~ a_truth(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truthtellers_and_normal_tell_truth) ).
fof(f6_nnf,plain,
! [X,Y] :
( a_truth(normal(Y))
| a_truth(truthteller(Y))
| ~ a_truth(says(Y,X))
| ~ a_truth(X) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( a_truth(normal(Y))
| a_truth(truthteller(Y))
| ~ a_truth(says(Y,X))
| ~ a_truth(X) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( a_truth(normal(X1))
| a_truth(truthteller(X1))
| ~ a_truth(says(X1,X0))
| ~ a_truth(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f9,axiom,
( a_truth(normal(X))
| a_truth(not_normal(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',normal_or_not_normal) ).
fof(f9_nnf,plain,
! [X] :
( a_truth(normal(X))
| a_truth(not_normal(X)) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] :
( a_truth(normal(X))
| a_truth(not_normal(X)) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( a_truth(normal(X0))
| a_truth(not_normal(X0)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p31,plain,
( a_truth(normal(X1))
| a_truth(normal(X0))
| a_truth(truthteller(X0))
| ~ a_truth(says(X0,not_normal(X1))) ),
inference(resolution,[status(thm)],[c6,c9]) ).
cnf(f21,hypothesis,
a_truth(says(c,not_normal(c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_says_c_not_normal) ).
fof(f21_nnf,plain,
a_truth(says(c,not_normal(c))),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
a_truth(says(c,not_normal(c))),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(p81,plain,
( a_truth(normal(c))
| a_truth(normal(c))
| a_truth(truthteller(c)) ),
inference(resolution,[status(thm)],[p31,c21]) ).
cnf(p82,plain,
( a_truth(normal(c))
| a_truth(truthteller(c)) ),
inference(factoring,[status(thm)],[p81]) ).
cnf(f14,axiom,
( ~ a_truth(normal(Y))
| ~ a_truth(normal(X))
| ~ people(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_two_normal1) ).
fof(f14_nnf,plain,
! [X,Y,Z] :
( ~ a_truth(normal(Y))
| ~ a_truth(normal(X))
| ~ people(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,Y,Z] :
( ~ a_truth(normal(Y))
| ~ a_truth(normal(X))
| ~ people(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( ~ a_truth(normal(X1))
| ~ a_truth(normal(X0))
| ~ people(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(f17,hypothesis,
people(b,c,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_c_a_are_people) ).
fof(f17_nnf,plain,
people(b,c,a),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
people(b,c,a),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(p48,plain,
( ~ a_truth(normal(c))
| ~ a_truth(normal(b)) ),
inference(resolution,[status(thm)],[c14,c17]) ).
cnf(f0,axiom,
( a_truth(normal(X))
| a_truth(liar(X))
| a_truth(truthteller(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',person_is_one_type) ).
fof(f0_nnf,plain,
! [X] :
( a_truth(normal(X))
| a_truth(liar(X))
| a_truth(truthteller(X)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] :
( a_truth(normal(X))
| a_truth(liar(X))
| a_truth(truthteller(X)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( a_truth(normal(X0))
| a_truth(liar(X0))
| a_truth(truthteller(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p51,plain,
( a_truth(liar(b))
| a_truth(truthteller(b))
| ~ a_truth(normal(c)) ),
inference(resolution,[status(thm)],[p48,c0]) ).
cnf(p85,plain,
( a_truth(liar(b))
| a_truth(truthteller(b))
| a_truth(truthteller(c)) ),
inference(resolution,[status(thm)],[p82,p51]) ).
cnf(f15,axiom,
( ~ a_truth(normal(Z))
| ~ a_truth(normal(X))
| ~ people(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_two_normal2) ).
fof(f15_nnf,plain,
! [X,Y,Z] :
( ~ a_truth(normal(Z))
| ~ a_truth(normal(X))
| ~ people(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y,Z] :
( ~ a_truth(normal(Z))
| ~ a_truth(normal(X))
| ~ people(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( ~ a_truth(normal(X2))
| ~ a_truth(normal(X0))
| ~ people(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(f16,hypothesis,
people(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_b_c_are_people) ).
fof(f16_nnf,plain,
people(a,b,c),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
people(a,b,c),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(p55,plain,
( ~ a_truth(normal(c))
| ~ a_truth(normal(a)) ),
inference(resolution,[status(thm)],[c15,c16]) ).
cnf(f7,axiom,
( a_truth(normal(Y))
| a_truth(liar(Y))
| ~ a_truth(says(Y,X))
| a_truth(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',liars_and_normal_lie) ).
fof(f7_nnf,plain,
! [X,Y] :
( a_truth(normal(Y))
| a_truth(liar(Y))
| ~ a_truth(says(Y,X))
| a_truth(X) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( a_truth(normal(Y))
| a_truth(liar(Y))
| ~ a_truth(says(Y,X))
| a_truth(X) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( a_truth(normal(X1))
| a_truth(liar(X1))
| ~ a_truth(says(X1,X0))
| a_truth(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(f19,hypothesis,
a_truth(says(a,normal(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_says_a_normal) ).
fof(f19_nnf,plain,
a_truth(says(a,normal(a))),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
a_truth(says(a,normal(a))),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(p36,plain,
( a_truth(normal(a))
| a_truth(liar(a))
| a_truth(normal(a)) ),
inference(resolution,[status(thm)],[c7,c19]) ).
cnf(p38,plain,
( a_truth(liar(a))
| a_truth(normal(a)) ),
inference(factoring,[status(thm)],[p36]) ).
cnf(p57,plain,
( a_truth(liar(a))
| ~ a_truth(normal(c)) ),
inference(resolution,[status(thm)],[p55,p38]) ).
cnf(p84,plain,
( a_truth(liar(a))
| a_truth(truthteller(c)) ),
inference(resolution,[status(thm)],[p82,p57]) ).
cnf(f12,axiom,
( ~ a_truth(liar(Y))
| ~ a_truth(liar(X))
| ~ people(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_two_liars1) ).
fof(f12_nnf,plain,
! [X,Y,Z] :
( ~ a_truth(liar(Y))
| ~ a_truth(liar(X))
| ~ people(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,Z] :
( ~ a_truth(liar(Y))
| ~ a_truth(liar(X))
| ~ people(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( ~ a_truth(liar(X1))
| ~ a_truth(liar(X0))
| ~ people(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p42,plain,
( ~ a_truth(liar(b))
| ~ a_truth(liar(a)) ),
inference(resolution,[status(thm)],[c12,c16]) ).
cnf(p92,plain,
( ~ a_truth(liar(b))
| a_truth(truthteller(c)) ),
inference(resolution,[status(thm)],[p84,p42]) ).
cnf(p103,plain,
( a_truth(truthteller(c))
| a_truth(truthteller(b))
| a_truth(truthteller(c)) ),
inference(resolution,[status(thm)],[p85,p92]) ).
cnf(p111,plain,
( a_truth(truthteller(b))
| a_truth(truthteller(c)) ),
inference(factoring,[status(thm)],[p103]) ).
cnf(p47,plain,
( ~ a_truth(normal(b))
| ~ a_truth(normal(a)) ),
inference(resolution,[status(thm)],[c14,c16]) ).
cnf(p50,plain,
( a_truth(liar(a))
| ~ a_truth(normal(b)) ),
inference(resolution,[status(thm)],[p47,p38]) ).
cnf(p53,plain,
( a_truth(liar(b))
| a_truth(truthteller(b))
| a_truth(liar(a)) ),
inference(resolution,[status(thm)],[p50,c0]) ).
cnf(f22,negated_conjecture,
( ~ a_truth(truthteller(Truthteller))
| ~ a_truth(normal(Normal))
| ~ a_truth(liar(Liar)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_one_of_each) ).
fof(f22_nnf,plain,
! [Liar,Normal,Truthteller] :
( ~ a_truth(truthteller(Truthteller))
| ~ a_truth(normal(Normal))
| ~ a_truth(liar(Liar)) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [Liar,Normal,Truthteller] :
( ~ a_truth(truthteller(Truthteller))
| ~ a_truth(normal(Normal))
| ~ a_truth(liar(Liar)) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( ~ a_truth(truthteller(X2))
| ~ a_truth(normal(X1))
| ~ a_truth(liar(X0)) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p62,plain,
( ~ a_truth(truthteller(X1))
| ~ a_truth(normal(X0))
| a_truth(truthteller(b))
| a_truth(liar(a)) ),
inference(resolution,[status(thm)],[p53,c22]) ).
cnf(p68,plain,
( a_truth(liar(a))
| ~ a_truth(truthteller(X0))
| a_truth(truthteller(b))
| a_truth(liar(a)) ),
inference(resolution,[status(thm)],[p62,p38]) ).
cnf(p69,plain,
( ~ a_truth(truthteller(X0))
| a_truth(truthteller(b))
| a_truth(liar(a)) ),
inference(factoring,[status(thm)],[p68]) ).
cnf(p116,plain,
( a_truth(truthteller(b))
| a_truth(liar(a))
| a_truth(truthteller(b)) ),
inference(resolution,[status(thm)],[p111,p69]) ).
cnf(p117,plain,
( a_truth(liar(a))
| a_truth(truthteller(b)) ),
inference(factoring,[status(thm)],[p116]) ).
cnf(p118,plain,
( ~ a_truth(truthteller(X1))
| ~ a_truth(normal(X0))
| a_truth(truthteller(b)) ),
inference(resolution,[status(thm)],[p117,c22]) ).
cnf(p124,plain,
( a_truth(liar(X1))
| a_truth(truthteller(X1))
| ~ a_truth(truthteller(X0))
| a_truth(truthteller(b)) ),
inference(resolution,[status(thm)],[p118,c0]) ).
cnf(p126,plain,
( a_truth(liar(b))
| ~ a_truth(truthteller(X0))
| a_truth(truthteller(b)) ),
inference(factoring,[status(thm)],[p124]) ).
cnf(p128,plain,
( a_truth(truthteller(b))
| a_truth(liar(b))
| a_truth(truthteller(b)) ),
inference(resolution,[status(thm)],[p126,p111]) ).
cnf(p129,plain,
( a_truth(liar(b))
| a_truth(truthteller(b)) ),
inference(factoring,[status(thm)],[p128]) ).
cnf(p123,plain,
( ~ a_truth(liar(b))
| a_truth(truthteller(b)) ),
inference(resolution,[status(thm)],[p117,p42]) ).
cnf(p134,plain,
( a_truth(truthteller(b))
| a_truth(truthteller(b)) ),
inference(resolution,[status(thm)],[p129,p123]) ).
cnf(p135,plain,
a_truth(truthteller(b)),
inference(factoring,[status(thm)],[p134]) ).
cnf(p87,plain,
( ~ a_truth(truthteller(X1))
| ~ a_truth(normal(X0))
| a_truth(truthteller(c)) ),
inference(resolution,[status(thm)],[p84,c22]) ).
cnf(p95,plain,
( a_truth(truthteller(c))
| ~ a_truth(truthteller(X0))
| a_truth(truthteller(c)) ),
inference(resolution,[status(thm)],[p87,p82]) ).
cnf(p97,plain,
( ~ a_truth(truthteller(X0))
| a_truth(truthteller(c)) ),
inference(factoring,[status(thm)],[p95]) ).
cnf(p141,plain,
a_truth(truthteller(c)),
inference(resolution,[status(thm)],[p135,p97]) ).
cnf(f10,axiom,
( ~ a_truth(truthteller(Y))
| ~ a_truth(truthteller(X))
| ~ people(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_two_truthtellers1) ).
fof(f10_nnf,plain,
! [X,Y,Z] :
( ~ a_truth(truthteller(Y))
| ~ a_truth(truthteller(X))
| ~ people(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,Z] :
( ~ a_truth(truthteller(Y))
| ~ a_truth(truthteller(X))
| ~ people(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( ~ a_truth(truthteller(X1))
| ~ a_truth(truthteller(X0))
| ~ people(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p26,plain,
( ~ a_truth(truthteller(c))
| ~ a_truth(truthteller(b)) ),
inference(resolution,[status(thm)],[c10,c17]) ).
cnf(p139,plain,
~ a_truth(truthteller(c)),
inference(resolution,[status(thm)],[p135,p26]) ).
cnf(p147,plain,
$false,
inference(resolution,[status(thm)],[p141,p139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ026-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 06:42:13 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.36/0.77 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.36/0.77 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------