%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PUZ023-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 4.75s 1.11s
% Output : Proof 4.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 9 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 101 ( 44 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
( a_truth(truthteller(Truthteller))
| ~ a_truth(says(Truthteller,Statement))
| ~ a_truth(Statement) ),
file('/export/starexec/sandbox2/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/sandbox2/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(p31,plain,
( a_truth(truthteller(X1))
| a_truth(truthteller(X0))
| ~ a_truth(says(X0,liar(X1))) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(f16,hypothesis,
a_truth(says(c,liar(b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_says_b_lies) ).
fof(f16_nnf,plain,
a_truth(says(c,liar(b))),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
a_truth(says(c,liar(b))),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(p90,plain,
( a_truth(truthteller(b))
| a_truth(truthteller(c)) ),
inference(resolution,[status(thm)],[p31,c16]) ).
cnf(f18,hypothesis,
( an_answer(b_liar_and_c_truthteller)
| ~ a_truth(truthteller(c))
| ~ a_truth(liar(b)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_liar_and_c_truthteller) ).
fof(f18_nnf,plain,
( an_answer(b_liar_and_c_truthteller)
| ~ a_truth(truthteller(c))
| ~ a_truth(liar(b)) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
( an_answer(b_liar_and_c_truthteller)
| ~ a_truth(truthteller(c))
| ~ a_truth(liar(b)) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( an_answer(b_liar_and_c_truthteller)
| ~ a_truth(truthteller(c))
| ~ a_truth(liar(b)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p23,plain,
( a_truth(truthteller(b))
| an_answer(b_liar_and_c_truthteller)
| ~ a_truth(truthteller(c)) ),
inference(resolution,[status(thm)],[c18,c0]) ).
cnf(p93,plain,
( a_truth(truthteller(b))
| an_answer(b_liar_and_c_truthteller)
| a_truth(truthteller(b)) ),
inference(resolution,[status(thm)],[p90,p23]) ).
cnf(p95,plain,
( an_answer(b_liar_and_c_truthteller)
| a_truth(truthteller(b)) ),
inference(factoring,[status(thm)],[p93]) ).
cnf(f19,hypothesis,
( an_answer(b_truthteller_and_c_liar)
| ~ a_truth(liar(c))
| ~ a_truth(truthteller(b)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_truthteller_and_c_liar) ).
fof(f19_nnf,plain,
( an_answer(b_truthteller_and_c_liar)
| ~ a_truth(liar(c))
| ~ a_truth(truthteller(b)) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
( an_answer(b_truthteller_and_c_liar)
| ~ a_truth(liar(c))
| ~ a_truth(truthteller(b)) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( an_answer(b_truthteller_and_c_liar)
| ~ a_truth(liar(c))
| ~ a_truth(truthteller(b)) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p98,plain,
( an_answer(b_truthteller_and_c_liar)
| ~ a_truth(liar(c))
| an_answer(b_liar_and_c_truthteller) ),
inference(resolution,[status(thm)],[p95,c19]) ).
cnf(f5,axiom,
( a_truth(liar(Liar))
| ~ a_truth(says(Liar,Statement))
| a_truth(Statement) ),
file('/export/starexec/sandbox2/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(p36,plain,
( a_truth(liar(c))
| a_truth(liar(b)) ),
inference(resolution,[status(thm)],[c5,c16]) ).
cnf(p105,plain,
( a_truth(liar(b))
| an_answer(b_truthteller_and_c_liar)
| an_answer(b_liar_and_c_truthteller) ),
inference(resolution,[status(thm)],[p98,p36]) ).
cnf(f1,axiom,
( ~ a_truth(liar(X))
| ~ a_truth(truthteller(X)) ),
file('/export/starexec/sandbox2/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(p96,plain,
( ~ a_truth(liar(b))
| an_answer(b_liar_and_c_truthteller) ),
inference(resolution,[status(thm)],[p95,c1]) ).
cnf(p117,plain,
( an_answer(b_liar_and_c_truthteller)
| an_answer(b_truthteller_and_c_liar)
| an_answer(b_liar_and_c_truthteller) ),
inference(resolution,[status(thm)],[p105,p96]) ).
cnf(p118,plain,
( an_answer(b_truthteller_and_c_liar)
| an_answer(b_liar_and_c_truthteller) ),
inference(factoring,[status(thm)],[p117]) ).
cnf(f21,negated_conjecture,
~ an_answer(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_an_answer) ).
fof(f21_nnf,plain,
! [X] : ~ an_answer(X),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X] : ~ an_answer(X),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
~ an_answer(X0),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p119,plain,
an_answer(b_liar_and_c_truthteller),
inference(resolution,[status(thm)],[p118,c21]) ).
cnf(p120,plain,
$false,
inference(resolution,[status(thm)],[p119,c21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ023-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 06:43:26 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.75/1.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.75/1.11 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------