%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PUZ027-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 5.27s 1.44s
% Output : Proof 5.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 14
% Syntax : Number of formulae : 101 ( 12 unt; 0 def)
% Number of atoms : 302 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 302 ( 101 ~; 201 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 77 ( 8 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f19,axiom,
( a_truth(lower(Y,X))
| a_truth(normal(Y))
| ~ a_truth(normal(X))
| ~ a_truth(not_lower(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_lower_than_normal) ).
fof(f19_nnf,plain,
! [X,Y] :
( a_truth(lower(Y,X))
| a_truth(normal(Y))
| ~ a_truth(normal(X))
| ~ a_truth(not_lower(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X,Y] :
( a_truth(lower(Y,X))
| a_truth(normal(Y))
| ~ a_truth(normal(X))
| ~ a_truth(not_lower(X,Y)) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( a_truth(lower(X1,X0))
| a_truth(normal(X1))
| ~ a_truth(normal(X0))
| ~ a_truth(not_lower(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
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(f21,hypothesis,
a_truth(says(b,not_lower(a,b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_says_a_not_lower_than_b) ).
fof(f21_nnf,plain,
a_truth(says(b,not_lower(a,b))),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
a_truth(says(b,not_lower(a,b))),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(p46,plain,
( a_truth(normal(b))
| a_truth(liar(b))
| a_truth(not_lower(a,b)) ),
inference(resolution,[status(thm)],[c7,c21]) ).
cnf(p65,plain,
( a_truth(normal(b))
| a_truth(liar(b))
| a_truth(lower(b,a))
| a_truth(normal(b))
| ~ a_truth(normal(a)) ),
inference(resolution,[status(thm)],[c19,p46]) ).
cnf(p116,plain,
( a_truth(liar(b))
| a_truth(lower(b,a))
| a_truth(normal(b))
| ~ a_truth(normal(a)) ),
inference(factoring,[status(thm)],[p65]) ).
cnf(f9,axiom,
( ~ a_truth(lower(X,Y))
| ~ a_truth(not_lower(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_not_lower_and_lower) ).
fof(f9_nnf,plain,
! [X,Y] :
( ~ a_truth(lower(X,Y))
| ~ a_truth(not_lower(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] :
( ~ a_truth(lower(X,Y))
| ~ a_truth(not_lower(X,Y)) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ a_truth(lower(X0,X1))
| ~ a_truth(not_lower(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p57,plain,
( ~ a_truth(lower(a,b))
| a_truth(normal(b))
| a_truth(liar(b)) ),
inference(resolution,[status(thm)],[p46,c9]) ).
cnf(f20,hypothesis,
a_truth(says(a,lower(a,b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_says_a_lower_than_b) ).
fof(f20_nnf,plain,
a_truth(says(a,lower(a,b))),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
a_truth(says(a,lower(a,b))),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(p45,plain,
( a_truth(normal(a))
| a_truth(liar(a))
| a_truth(lower(a,b)) ),
inference(resolution,[status(thm)],[c7,c20]) ).
cnf(p61,plain,
( a_truth(normal(a))
| a_truth(liar(a))
| a_truth(normal(b))
| a_truth(liar(b)) ),
inference(resolution,[status(thm)],[p57,p45]) ).
cnf(f15,axiom,
( a_truth(liar(X))
| ~ a_truth(normal(Y))
| ~ a_truth(lower(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',liars_lower_than_normal) ).
fof(f15_nnf,plain,
! [X,Y] :
( a_truth(liar(X))
| ~ a_truth(normal(Y))
| ~ a_truth(lower(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y] :
( a_truth(liar(X))
| ~ a_truth(normal(Y))
| ~ a_truth(lower(X,Y)) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( a_truth(liar(X0))
| ~ a_truth(normal(X1))
| ~ a_truth(lower(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p54,plain,
( a_truth(liar(a))
| ~ a_truth(normal(b))
| a_truth(normal(a))
| a_truth(liar(a)) ),
inference(resolution,[status(thm)],[p45,c15]) ).
cnf(p64,plain,
( ~ a_truth(normal(b))
| a_truth(normal(a))
| a_truth(liar(a)) ),
inference(factoring,[status(thm)],[p54]) ).
cnf(p70,plain,
( a_truth(normal(a))
| a_truth(liar(a))
| a_truth(normal(a))
| a_truth(liar(a))
| a_truth(liar(b)) ),
inference(resolution,[status(thm)],[p61,p64]) ).
cnf(p95,plain,
( a_truth(normal(a))
| a_truth(normal(a))
| a_truth(liar(a))
| a_truth(liar(b)) ),
inference(factoring,[status(thm)],[p70]) ).
cnf(p97,plain,
( a_truth(normal(a))
| a_truth(liar(a))
| a_truth(liar(b)) ),
inference(factoring,[status(thm)],[p95]) ).
cnf(p118,plain,
( a_truth(liar(a))
| a_truth(liar(b))
| a_truth(liar(b))
| a_truth(lower(b,a))
| a_truth(normal(b)) ),
inference(resolution,[status(thm)],[p116,p97]) ).
cnf(p171,plain,
( a_truth(liar(a))
| a_truth(liar(b))
| a_truth(lower(b,a))
| a_truth(normal(b)) ),
inference(factoring,[status(thm)],[p118]) ).
cnf(f10,axiom,
( a_truth(lower(X,Y))
| a_truth(not_lower(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_lower_or_lower) ).
fof(f10_nnf,plain,
! [X,Y] :
( a_truth(lower(X,Y))
| a_truth(not_lower(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y] :
( a_truth(lower(X,Y))
| a_truth(not_lower(X,Y)) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( a_truth(lower(X0,X1))
| a_truth(not_lower(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p50,plain,
( a_truth(not_lower(X1,X0))
| a_truth(liar(X1))
| ~ a_truth(normal(X0)) ),
inference(resolution,[status(thm)],[c15,c10]) ).
cnf(p102,plain,
( a_truth(not_lower(X0,a))
| a_truth(liar(X0))
| a_truth(liar(a))
| a_truth(liar(b)) ),
inference(resolution,[status(thm)],[p97,p50]) ).
cnf(p108,plain,
( a_truth(not_lower(b,a))
| a_truth(liar(a))
| a_truth(liar(b)) ),
inference(factoring,[status(thm)],[p102]) ).
cnf(p113,plain,
( ~ a_truth(lower(b,a))
| a_truth(liar(a))
| a_truth(liar(b)) ),
inference(resolution,[status(thm)],[p108,c9]) ).
cnf(p176,plain,
( a_truth(liar(a))
| a_truth(liar(b))
| a_truth(liar(a))
| a_truth(liar(b))
| a_truth(normal(b)) ),
inference(resolution,[status(thm)],[p171,p113]) ).
cnf(p180,plain,
( a_truth(liar(a))
| a_truth(liar(a))
| a_truth(liar(b))
| a_truth(normal(b)) ),
inference(factoring,[status(thm)],[p176]) ).
cnf(p182,plain,
( a_truth(liar(a))
| a_truth(liar(b))
| a_truth(normal(b)) ),
inference(factoring,[status(thm)],[p180]) ).
cnf(f26,hypothesis,
( answer(a_and_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(normal(a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_and_b_normal) ).
fof(f26_nnf,plain,
( answer(a_and_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(normal(a)) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
( answer(a_and_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(normal(a)) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
( answer(a_and_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(normal(a)) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p100,plain,
( answer(a_and_b_normal)
| ~ a_truth(normal(b))
| a_truth(liar(a))
| a_truth(liar(b)) ),
inference(resolution,[status(thm)],[p97,c26]) ).
cnf(p188,plain,
( answer(a_and_b_normal)
| a_truth(liar(a))
| a_truth(liar(b))
| a_truth(liar(a))
| a_truth(liar(b)) ),
inference(resolution,[status(thm)],[p182,p100]) ).
cnf(p212,plain,
( answer(a_and_b_normal)
| a_truth(liar(a))
| a_truth(liar(a))
| a_truth(liar(b)) ),
inference(factoring,[status(thm)],[p188]) ).
cnf(p214,plain,
( answer(a_and_b_normal)
| a_truth(liar(a))
| a_truth(liar(b)) ),
inference(factoring,[status(thm)],[p212]) ).
cnf(f5,axiom,
( ~ a_truth(Y)
| ~ a_truth(says(X,Y))
| ~ a_truth(liar(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',liars_lie) ).
fof(f5_nnf,plain,
! [X,Y] :
( ~ a_truth(Y)
| ~ a_truth(says(X,Y))
| ~ a_truth(liar(X)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( ~ a_truth(Y)
| ~ a_truth(says(X,Y))
| ~ a_truth(liar(X)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ a_truth(X1)
| ~ a_truth(says(X0,X1))
| ~ a_truth(liar(X0)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p216,plain,
( ~ a_truth(X0)
| ~ a_truth(says(b,X0))
| answer(a_and_b_normal)
| a_truth(liar(a)) ),
inference(resolution,[status(thm)],[p214,c5]) ).
cnf(p230,plain,
( ~ a_truth(not_lower(a,b))
| answer(a_and_b_normal)
| a_truth(liar(a)) ),
inference(resolution,[status(thm)],[p216,c21]) ).
cnf(f16,axiom,
( ~ a_truth(liar(Y))
| ~ a_truth(lower(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_one_lower_than_liars) ).
fof(f16_nnf,plain,
! [X,Y] :
( ~ a_truth(liar(Y))
| ~ a_truth(lower(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y] :
( ~ a_truth(liar(Y))
| ~ a_truth(lower(X,Y)) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ~ a_truth(liar(X1))
| ~ a_truth(lower(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p34,plain,
( ~ a_truth(liar(X1))
| a_truth(not_lower(X0,X1)) ),
inference(resolution,[status(thm)],[c10,c16]) ).
cnf(p217,plain,
( a_truth(not_lower(X0,b))
| answer(a_and_b_normal)
| a_truth(liar(a)) ),
inference(resolution,[status(thm)],[p214,p34]) ).
cnf(p233,plain,
( answer(a_and_b_normal)
| a_truth(liar(a))
| answer(a_and_b_normal)
| a_truth(liar(a)) ),
inference(resolution,[status(thm)],[p230,p217]) ).
cnf(p234,plain,
( answer(a_and_b_normal)
| answer(a_and_b_normal)
| a_truth(liar(a)) ),
inference(factoring,[status(thm)],[p233]) ).
cnf(p236,plain,
( answer(a_and_b_normal)
| a_truth(liar(a)) ),
inference(factoring,[status(thm)],[p234]) ).
cnf(f18,axiom,
( a_truth(lower(Y,X))
| a_truth(liar(Y))
| ~ a_truth(liar(X))
| ~ a_truth(not_lower(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_lower_than_liar) ).
fof(f18_nnf,plain,
! [X,Y] :
( a_truth(lower(Y,X))
| a_truth(liar(Y))
| ~ a_truth(liar(X))
| ~ a_truth(not_lower(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y] :
( a_truth(lower(Y,X))
| a_truth(liar(Y))
| ~ a_truth(liar(X))
| ~ a_truth(not_lower(X,Y)) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( a_truth(lower(X1,X0))
| a_truth(liar(X1))
| ~ a_truth(liar(X0))
| ~ a_truth(not_lower(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p62,plain,
( a_truth(normal(b))
| a_truth(liar(b))
| a_truth(lower(b,a))
| a_truth(liar(b))
| ~ a_truth(liar(a)) ),
inference(resolution,[status(thm)],[c18,p46]) ).
cnf(p112,plain,
( a_truth(normal(b))
| a_truth(lower(b,a))
| a_truth(liar(b))
| ~ a_truth(liar(a)) ),
inference(factoring,[status(thm)],[p62]) ).
cnf(p246,plain,
( a_truth(normal(b))
| a_truth(lower(b,a))
| a_truth(liar(b))
| answer(a_and_b_normal) ),
inference(resolution,[status(thm)],[p236,p112]) ).
cnf(p239,plain,
( a_truth(not_lower(X0,a))
| answer(a_and_b_normal) ),
inference(resolution,[status(thm)],[p236,p34]) ).
cnf(p248,plain,
( ~ a_truth(lower(X0,a))
| answer(a_and_b_normal) ),
inference(resolution,[status(thm)],[p239,c9]) ).
cnf(p284,plain,
( answer(a_and_b_normal)
| a_truth(normal(b))
| a_truth(liar(b))
| answer(a_and_b_normal) ),
inference(resolution,[status(thm)],[p246,p248]) ).
cnf(p285,plain,
( a_truth(normal(b))
| a_truth(liar(b))
| answer(a_and_b_normal) ),
inference(factoring,[status(thm)],[p284]) ).
cnf(f29,hypothesis,
( answer(a_liar_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(liar(a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_liar_b_normal) ).
fof(f29_nnf,plain,
( answer(a_liar_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(liar(a)) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
( answer(a_liar_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(liar(a)) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( answer(a_liar_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(liar(a)) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p243,plain,
( answer(a_liar_b_normal)
| ~ a_truth(normal(b))
| answer(a_and_b_normal) ),
inference(resolution,[status(thm)],[p236,c29]) ).
cnf(p291,plain,
( answer(a_liar_b_normal)
| answer(a_and_b_normal)
| a_truth(liar(b))
| answer(a_and_b_normal) ),
inference(resolution,[status(thm)],[p285,p243]) ).
cnf(p292,plain,
( answer(a_liar_b_normal)
| a_truth(liar(b))
| answer(a_and_b_normal) ),
inference(factoring,[status(thm)],[p291]) ).
cnf(f30,hypothesis,
( answer(a_and_b_liar)
| ~ a_truth(liar(b))
| ~ a_truth(liar(a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_and_b_liar) ).
fof(f30_nnf,plain,
( answer(a_and_b_liar)
| ~ a_truth(liar(b))
| ~ a_truth(liar(a)) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
( answer(a_and_b_liar)
| ~ a_truth(liar(b))
| ~ a_truth(liar(a)) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( answer(a_and_b_liar)
| ~ a_truth(liar(b))
| ~ a_truth(liar(a)) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p244,plain,
( answer(a_and_b_liar)
| ~ a_truth(liar(b))
| answer(a_and_b_normal) ),
inference(resolution,[status(thm)],[p236,c30]) ).
cnf(p298,plain,
( answer(a_and_b_liar)
| answer(a_and_b_normal)
| answer(a_liar_b_normal)
| answer(a_and_b_normal) ),
inference(resolution,[status(thm)],[p292,p244]) ).
cnf(p308,plain,
( answer(a_and_b_liar)
| answer(a_liar_b_normal)
| answer(a_and_b_normal) ),
inference(factoring,[status(thm)],[p298]) ).
cnf(f31,negated_conjecture,
~ answer(Answer),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_an_answer) ).
fof(f31_nnf,plain,
! [Answer] : ~ answer(Answer),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [Answer] : ~ answer(Answer),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c31,plain,
~ answer(X0),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p309,plain,
( answer(a_liar_b_normal)
| answer(a_and_b_normal) ),
inference(resolution,[status(thm)],[p308,c31]) ).
cnf(p313,plain,
answer(a_and_b_normal),
inference(resolution,[status(thm)],[p309,c31]) ).
cnf(p314,plain,
$false,
inference(resolution,[status(thm)],[p313,c31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ027-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.33 % Computer : n001.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Thu Sep 24 06:47:37 UTC 2026
% 0.08/0.33 % CPUTime :
% 0.08/0.33 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.27/1.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.27/1.44 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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