%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PUZ032-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 02:31:55 PM UTC 2026
% Result : Unsatisfiable 4.64s 6.10s
% Output : Proof 4.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 84 ( 43 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
( a_truth(truthteller(Truthteller))
| ~ a_truth(says(Truthteller,Statement))
| ~ a_truth(Statement) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truths_are_told_by_truthtellers) ).
fof(f4_nnf,plain,
! [Statement,Truthteller] :
( a_truth(truthteller(Truthteller))
| ~ a_truth(says(Truthteller,Statement))
| ~ a_truth(Statement) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [Statement,Truthteller] :
( a_truth(truthteller(Truthteller))
| ~ a_truth(says(Truthteller,Statement))
| ~ a_truth(Statement) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( a_truth(truthteller(X1))
| ~ a_truth(says(X1,X0))
| ~ a_truth(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f0,axiom,
( a_truth(liar(X))
| a_truth(truthteller(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truthteller_or_liar) ).
fof(f0_nnf,plain,
! [X] :
( a_truth(liar(X))
| a_truth(truthteller(X)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] :
( a_truth(liar(X))
| a_truth(truthteller(X)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( a_truth(liar(X0))
| a_truth(truthteller(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p14,plain,
( a_truth(truthteller(X1))
| a_truth(truthteller(X0))
| ~ a_truth(says(X0,liar(X1))) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(f8,hypothesis,
a_truth(says(c,liar(b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_says_b_is_a_liar) ).
fof(f8_nnf,plain,
a_truth(says(c,liar(b))),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
a_truth(says(c,liar(b))),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(p31,plain,
( a_truth(truthteller(b))
| a_truth(truthteller(c)) ),
inference(resolution,[status(thm)],[p14,c8]) ).
cnf(f9,negated_conjecture,
~ a_truth(truthteller(c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_is_a_truthteller) ).
fof(f9_nnf,plain,
~ a_truth(truthteller(c)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ a_truth(truthteller(c)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ a_truth(truthteller(c)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p41,plain,
a_truth(truthteller(b)),
inference(resolution,[status(thm)],[p31,c9]) ).
cnf(f1,axiom,
( ~ a_truth(liar(X))
| ~ a_truth(truthteller(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_both) ).
fof(f1_nnf,plain,
! [X] :
( ~ a_truth(liar(X))
| ~ a_truth(truthteller(X)) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] :
( ~ a_truth(liar(X))
| ~ a_truth(truthteller(X)) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ a_truth(liar(X0))
| ~ a_truth(truthteller(X0)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p42,plain,
~ a_truth(liar(b)),
inference(resolution,[status(thm)],[p41,c1]) ).
cnf(f5,axiom,
( a_truth(liar(Liar))
| ~ a_truth(says(Liar,Statement))
| a_truth(Statement) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',liars_are_told_by_liars) ).
fof(f5_nnf,plain,
! [Statement,Liar] :
( a_truth(liar(Liar))
| ~ a_truth(says(Liar,Statement))
| a_truth(Statement) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [Statement,Liar] :
( a_truth(liar(Liar))
| ~ a_truth(says(Liar,Statement))
| a_truth(Statement) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( a_truth(liar(X1))
| ~ a_truth(says(X1,X0))
| a_truth(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f7,hypothesis,
a_truth(says(b,says(a,liar(a)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_says_a_says_hes_a_liar) ).
fof(f7_nnf,plain,
a_truth(says(b,says(a,liar(a)))),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
a_truth(says(b,says(a,liar(a)))),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(p19,plain,
( a_truth(liar(b))
| a_truth(says(a,liar(a))) ),
inference(resolution,[status(thm)],[c5,c7]) ).
cnf(f3,axiom,
( ~ a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| ~ a_truth(liar(Liar)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',liars_lie) ).
fof(f3_nnf,plain,
! [Liar,Statement] :
( ~ a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| ~ a_truth(liar(Liar)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [Liar,Statement] :
( ~ a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| ~ a_truth(liar(Liar)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ a_truth(X1)
| ~ a_truth(says(X0,X1))
| ~ a_truth(liar(X0)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p10,plain,
( ~ a_truth(says(X0,liar(X0)))
| ~ a_truth(liar(X0)) ),
inference(factoring,[status(thm)],[c3]) ).
cnf(p11,plain,
( a_truth(truthteller(X0))
| ~ a_truth(says(X0,liar(X0))) ),
inference(resolution,[status(thm)],[p10,c0]) ).
cnf(p27,plain,
( a_truth(truthteller(a))
| a_truth(liar(b)) ),
inference(resolution,[status(thm)],[p19,p11]) ).
cnf(p46,plain,
a_truth(truthteller(a)),
inference(resolution,[status(thm)],[p42,p27]) ).
cnf(p49,plain,
~ a_truth(liar(a)),
inference(resolution,[status(thm)],[p46,c1]) ).
cnf(p16,plain,
( ~ a_truth(says(X0,liar(X0)))
| a_truth(liar(X0)) ),
inference(factoring,[status(thm)],[c5]) ).
cnf(p30,plain,
( a_truth(liar(a))
| a_truth(liar(b)) ),
inference(resolution,[status(thm)],[p19,p16]) ).
cnf(p47,plain,
a_truth(liar(a)),
inference(resolution,[status(thm)],[p42,p30]) ).
cnf(p55,plain,
$false,
inference(resolution,[status(thm)],[p49,p47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ032-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n018.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Thu Sep 24 06:45:23 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.64/6.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.64/6.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------