%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM766^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n017.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 : Wed Sep 30 08:18:09 AM UTC 2026
% Result : Theorem 25.16s 7.89s
% Output : Refutation 25.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 24 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 6 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 184 ( 18 ~; 0 |; 0 &; 154 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 2 ^; 47 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(frac_type,type,
frac: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: frac ).
thf(y_decl,type,
y: frac ).
thf(ts_decl,type,
ts: nat > nat > nat ).
thf(num_decl,type,
num: frac > nat ).
thf(den_decl,type,
den: frac > nat ).
thf(pl_decl,type,
pl: nat > nat > nat ).
thf(eq_decl,type,
eq: frac > frac > $o ).
thf(pf_decl,type,
pf: frac > frac > frac ).
thf(fr_decl,type,
fr: nat > nat > frac ).
thf(ind_decl,type,
ind: ( nat > $o ) > nat ).
thf(amone_decl,type,
amone: ( nat > $o ) > $o ).
thf(1,conjecture,
~ ! [A: frac] :
~ ( eq @ ( pf @ y @ A ) @ x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz67a) ).
thf(2,negated_conjecture,
~ ~ ! [A: frac] :
~ ( eq @ ( pf @ y @ A ) @ x ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ~ ! [A: frac] :
~ ( eq @ ( pf @ y @ A ) @ x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: nat > $o] :
( ~ ( ( amone @ A )
=> ~ ~ ! [B: nat] :
~ ( A @ B ) )
=> ( A @ ( ind @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oneax) ).
thf(39,plain,
! [A: nat > $o] :
( ~ ( ( amone @ A )
=> ! [B: nat] :
~ ( A @ B ) )
=> ( A @ ( ind @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(7,axiom,
! [A: frac,B: nat] : ( eq @ A @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40) ).
thf(30,plain,
! [A: frac,B: nat] : ( eq @ A @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz39) ).
thf(24,plain,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [A: nat,B: nat,C: nat] : ( eq @ ( pf @ ( fr @ A @ C ) @ ( fr @ B @ C ) ) @ ( fr @ ( pl @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz57) ).
thf(37,plain,
! [A: nat,B: nat,C: nat] : ( eq @ ( pf @ ( fr @ A @ C ) @ ( fr @ B @ C ) ) @ ( fr @ ( pl @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [A: frac,B: nat] : ( eq @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40a) ).
thf(45,plain,
! [A: frac,B: nat] : ( eq @ ( fr @ ( ts @ ( num @ A ) @ B ) @ ( ts @ ( den @ A ) @ B ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
~ ! [A: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
!= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(17,plain,
~ ! [A: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
!= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: frac] : ( eq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz37) ).
thf(32,plain,
! [A: frac] : ( eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz29) ).
thf(34,plain,
! [A: nat,B: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( amone
@ ^ [C: nat] :
( A
= ( pl @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz8b) ).
thf(22,plain,
! [A: nat,B: nat] :
( amone
@ ^ [C: nat] :
( A
= ( pl @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( eq @ A @ B )
=> ( ( eq @ C @ D )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz56) ).
thf(27,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( eq @ A @ B )
=> ( ( eq @ C @ D )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1993,plain,
$false,
inference(e,[status(thm)],[13,39,30,24,37,45,17,32,34,22,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM766^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.20 % Computer : n017.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 12:49:22 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.98 % [INFO] Parsing done (195ms).
% 1.17/1.00 % [INFO] Running in sequential loop mode.
% 2.01/1.41 % [INFO] eprover registered as external prover.
% 2.01/1.42 % [INFO] Scanning for conjecture ...
% 2.20/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.20/1.55 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.20/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.20/1.59 % [INFO] Type checking passed.
% 2.40/1.60 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 25.16/7.89 % External prover 'e' found a proof!
% 25.16/7.89 % [INFO] Killing All external provers ...
% 25.16/7.89 % Time passed: 7539ms (effective reasoning time: 6885ms)
% 25.16/7.89 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 25.16/7.89 % Axioms used in derivation (10): satz29, satz40a, satz39, m, oneax, satz56, satz40, satz57, satz8b, satz37
% 25.16/7.89 % No. of inferences in proof: 24
% 25.16/7.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7539 ms resp. 6885 ms w/o parsing
% 25.55/7.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.55/7.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------