%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ032-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:23:13 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 30
% Syntax : Number of formulae : 70 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 367 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 541 ( 250 ~; 257 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 142 ( 130 !; 0 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_truth_type,type,
a_truth: $i > $o ).
tff(says_type,type,
says: ( $i * $i ) > $i ).
tff(liar_type,type,
liar: $i > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(truthteller_type,type,
truthteller: $i > $i ).
tff(c_type,type,
c: $i ).
tff(1,plain,
( ~ a_truth(truthteller(c))
<=> ~ a_truth(truthteller(c)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ a_truth(truthteller(c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_is_a_truthteller) ).
tff(3,plain,
~ a_truth(truthteller(c)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( a_truth(says(c,liar(b)))
<=> a_truth(says(c,liar(b))) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
a_truth(says(c,liar(b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_says_b_is_a_liar) ).
tff(6,plain,
a_truth(says(c,liar(b))),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [Truthteller: $i,Statement: $i] :
refl(( ( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) )
<=> ( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) )
<=> ! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) )
<=> ! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [Truthteller: $i,Statement: $i] :
rewrite(( ( ~ a_truth(Statement)
| ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller)) )
<=> ( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Truthteller: $i,Statement: $i] :
( ~ a_truth(Statement)
| ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller)) )
<=> ! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [Truthteller: $i,Statement: $i] :
( ~ a_truth(Statement)
| ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ002-0.ax',truths_are_told_by_truthtellers) ).
tff(13,plain,
! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) )
| a_truth(truthteller(c))
| ~ a_truth(liar(b))
| ~ a_truth(says(c,liar(b))) )
<=> ( ~ ! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) )
| a_truth(truthteller(c))
| ~ a_truth(liar(b))
| ~ a_truth(says(c,liar(b))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ a_truth(says(c,liar(b)))
| a_truth(truthteller(c))
| ~ a_truth(liar(b)) )
<=> ( a_truth(truthteller(c))
| ~ a_truth(liar(b))
| ~ a_truth(says(c,liar(b))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) )
| ~ a_truth(says(c,liar(b)))
| a_truth(truthteller(c))
| ~ a_truth(liar(b)) )
<=> ( ~ ! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) )
| a_truth(truthteller(c))
| ~ a_truth(liar(b))
| ~ a_truth(says(c,liar(b))) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) )
| ~ a_truth(says(c,liar(b)))
| a_truth(truthteller(c))
| ~ a_truth(liar(b)) )
<=> ( ~ ! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) )
| a_truth(truthteller(c))
| ~ a_truth(liar(b))
| ~ a_truth(says(c,liar(b))) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) )
| ~ a_truth(says(c,liar(b)))
| a_truth(truthteller(c))
| ~ a_truth(liar(b)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [Truthteller: $i,Statement: $i] :
( ~ a_truth(says(Truthteller,Statement))
| a_truth(truthteller(Truthteller))
| ~ a_truth(Statement) )
| a_truth(truthteller(c))
| ~ a_truth(liar(b))
| ~ a_truth(says(c,liar(b))) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ a_truth(liar(b)),
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
tff(24,plain,
( a_truth(says(b,says(a,liar(a))))
<=> a_truth(says(b,says(a,liar(a)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
a_truth(says(b,says(a,liar(a)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_says_a_says_hes_a_liar) ).
tff(26,plain,
a_truth(says(b,says(a,liar(a)))),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
^ [Liar: $i,Statement: $i] :
refl(( ( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
<=> ( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
<=> ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
<=> ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
^ [Liar: $i,Statement: $i] :
rewrite(( ( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
<=> ( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
<=> ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ002-0.ax',liars_are_told_by_liars) ).
tff(33,plain,
! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(liar(b))
| a_truth(says(a,liar(a)))
| ~ a_truth(says(b,says(a,liar(a)))) )
<=> ( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(liar(b))
| a_truth(says(a,liar(a)))
| ~ a_truth(says(b,says(a,liar(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( a_truth(says(a,liar(a)))
| ~ a_truth(says(b,says(a,liar(a))))
| a_truth(liar(b)) )
<=> ( a_truth(liar(b))
| a_truth(says(a,liar(a)))
| ~ a_truth(says(b,says(a,liar(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(says(a,liar(a)))
| ~ a_truth(says(b,says(a,liar(a))))
| a_truth(liar(b)) )
<=> ( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(liar(b))
| a_truth(says(a,liar(a)))
| ~ a_truth(says(b,says(a,liar(a)))) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(says(a,liar(a)))
| ~ a_truth(says(b,says(a,liar(a))))
| a_truth(liar(b)) )
<=> ( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(liar(b))
| a_truth(says(a,liar(a)))
| ~ a_truth(says(b,says(a,liar(a)))) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(says(a,liar(a)))
| ~ a_truth(says(b,says(a,liar(a))))
| a_truth(liar(b)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(liar(b))
| a_truth(says(a,liar(a)))
| ~ a_truth(says(b,says(a,liar(a)))) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
( a_truth(liar(b))
| a_truth(says(a,liar(a))) ),
inference(unit_resolution,[status(thm)],[42,36,26]) ).
tff(44,plain,
a_truth(says(a,liar(a))),
inference(unit_resolution,[status(thm)],[43,23]) ).
tff(45,plain,
( ( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(liar(a))
| ~ a_truth(says(a,liar(a))) )
<=> ( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(liar(a))
| ~ a_truth(says(a,liar(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( a_truth(liar(a))
| ~ a_truth(says(a,liar(a)))
| a_truth(liar(a)) )
<=> ( a_truth(liar(a))
| ~ a_truth(says(a,liar(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(liar(a))
| ~ a_truth(says(a,liar(a)))
| a_truth(liar(a)) )
<=> ( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(liar(a))
| ~ a_truth(says(a,liar(a))) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(liar(a))
| ~ a_truth(says(a,liar(a)))
| a_truth(liar(a)) )
<=> ( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(liar(a))
| ~ a_truth(says(a,liar(a))) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(liar(a))
| ~ a_truth(says(a,liar(a)))
| a_truth(liar(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [Liar: $i,Statement: $i] :
( a_truth(Statement)
| ~ a_truth(says(Liar,Statement))
| a_truth(liar(Liar)) )
| a_truth(liar(a))
| ~ a_truth(says(a,liar(a))) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( a_truth(liar(a))
| ~ a_truth(says(a,liar(a))) ),
inference(unit_resolution,[status(thm)],[50,36]) ).
tff(52,plain,
a_truth(liar(a)),
inference(unit_resolution,[status(thm)],[51,44]) ).
tff(53,plain,
^ [Liar: $i,Statement: $i] :
refl(( ( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) )
<=> ( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) )
<=> ! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) )
<=> ! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
^ [Liar: $i,Statement: $i] :
rewrite(( ( ~ a_truth(liar(Liar))
| ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement) )
<=> ( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [Liar: $i,Statement: $i] :
( ~ a_truth(liar(Liar))
| ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement) )
<=> ! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,axiom,
! [Liar: $i,Statement: $i] :
( ~ a_truth(liar(Liar))
| ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ002-0.ax',liars_lie) ).
tff(59,plain,
! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) ),
inference(modus_ponens,[status(thm)],[61,54]) ).
tff(63,plain,
( ( ~ ! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) )
| ~ a_truth(liar(a))
| ~ a_truth(says(a,liar(a))) )
<=> ( ~ ! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) )
| ~ a_truth(liar(a))
| ~ a_truth(says(a,liar(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( ~ a_truth(says(a,liar(a)))
| ~ a_truth(liar(a))
| ~ a_truth(liar(a)) )
<=> ( ~ a_truth(liar(a))
| ~ a_truth(says(a,liar(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ( ~ ! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) )
| ~ a_truth(says(a,liar(a)))
| ~ a_truth(liar(a))
| ~ a_truth(liar(a)) )
<=> ( ~ ! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) )
| ~ a_truth(liar(a))
| ~ a_truth(says(a,liar(a))) ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ( ~ ! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) )
| ~ a_truth(says(a,liar(a)))
| ~ a_truth(liar(a))
| ~ a_truth(liar(a)) )
<=> ( ~ ! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) )
| ~ a_truth(liar(a))
| ~ a_truth(says(a,liar(a))) ) ),
inference(transitivity,[status(thm)],[65,63]) ).
tff(67,plain,
( ~ ! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) )
| ~ a_truth(says(a,liar(a)))
| ~ a_truth(liar(a))
| ~ a_truth(liar(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [Liar: $i,Statement: $i] :
( ~ a_truth(says(Liar,Statement))
| ~ a_truth(Statement)
| ~ a_truth(liar(Liar)) )
| ~ a_truth(liar(a))
| ~ a_truth(says(a,liar(a))) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
( ~ a_truth(liar(a))
| ~ a_truth(says(a,liar(a))) ),
inference(unit_resolution,[status(thm)],[68,62]) ).
tff(70,plain,
$false,
inference(unit_resolution,[status(thm)],[69,52,44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : PUZ032-1 : TPTP v9.0.0. Released v1.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 02:40:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Unsatisfiable
% 0.12/0.36 % SZS output start Proof
% See solution above
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------