%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM742^1 : 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 08:18:05 AM UTC 2026
% Result : Theorem 12.19s 4.23s
% Output : Refutation 12.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 131 ( 12 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 327 ( 45 ~; 43 |; 0 &; 220 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 75 ( 0 ^; 75 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(frac_type,type,
frac: $tType ).
thf(x_decl,type,
x: frac ).
thf(y_decl,type,
y: frac ).
thf(z_decl,type,
z: frac ).
thf(lessf_decl,type,
lessf: frac > frac > $o ).
thf(eq_decl,type,
eq: frac > frac > $o ).
thf(4,axiom,
lessf @ y @ z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
thf(13,plain,
lessf @ y @ z,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(11,plain,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
( ( lessf @ x @ y )
| ( eq @ x @ y ) ),
inference(cnf,[status(esa)],[11]) ).
thf(7,axiom,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ( eq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz38) ).
thf(18,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ( eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,plain,
! [B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ( eq @ B @ A ) ),
inference(cnf,[status(esa)],[18]) ).
thf(135,plain,
! [B: frac,A: frac] :
( ( lessf @ x @ y )
| ~ $true
| ( eq @ B @ A )
| ( ( eq @ x @ y )
!= ( eq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,19]) ).
thf(136,plain,
! [B: frac,A: frac] :
( ( lessf @ x @ y )
| ( eq @ B @ A )
| ( ( eq @ x @ y )
!= ( eq @ A @ B ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(137,plain,
( ( lessf @ x @ y )
| ( eq @ y @ x ) ),
inference(pattern_uni,[status(thm)],[136:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(8,axiom,
! [A: frac,B: frac,C: frac] :
( ( lessf @ A @ B )
=> ( ( lessf @ B @ C )
=> ( lessf @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz50) ).
thf(20,plain,
! [A: frac,B: frac,C: frac] :
( ( lessf @ A @ B )
=> ( ( lessf @ B @ C )
=> ( lessf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(21,plain,
! [A: frac,B: frac] :
( ( lessf @ A @ B )
=> ! [C: frac] :
( ( lessf @ B @ C )
=> ( lessf @ A @ C ) ) ),
inference(miniscope,[status(thm)],[20]) ).
thf(22,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ~ ( lessf @ B @ C )
| ( lessf @ A @ C ) ),
inference(cnf,[status(esa)],[21]) ).
thf(192,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ~ $true
| ( lessf @ A @ C )
| ( ( lessf @ y @ z )
!= ( lessf @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[13,22]) ).
thf(193,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ( lessf @ A @ C )
| ( ( lessf @ y @ z )
!= ( lessf @ B @ C ) ) ),
inference(simp,[status(thm)],[192]) ).
thf(194,plain,
! [A: frac] :
( ~ ( lessf @ A @ y )
| ( lessf @ A @ z ) ),
inference(pattern_uni,[status(thm)],[193:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
thf(1,conjecture,
lessf @ x @ z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz51a) ).
thf(2,negated_conjecture,
~ ( lessf @ x @ z ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ( lessf @ x @ z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(229,plain,
! [A: frac] :
( ~ ( lessf @ A @ y )
| ~ $true
| ( ( lessf @ A @ z )
!= ( lessf @ x @ z ) ) ),
inference(paramod_ordered,[status(thm)],[194,10]) ).
thf(230,plain,
! [A: frac] :
( ~ ( lessf @ A @ y )
| ( ( lessf @ A @ z )
!= ( lessf @ x @ z ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(231,plain,
~ ( lessf @ x @ y ),
inference(pattern_uni,[status(thm)],[230:[bind(A,$thf( x ))]]) ).
thf(264,plain,
( $false
| ( eq @ y @ x ) ),
inference(rewrite,[status(thm)],[137,231]) ).
thf(265,plain,
eq @ y @ x,
inference(simp,[status(thm)],[264]) ).
thf(9,axiom,
! [A: frac] : ( eq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz37) ).
thf(23,plain,
! [A: frac] : ( eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(24,plain,
! [A: frac] : ( eq @ A @ A ),
inference(cnf,[status(esa)],[23]) ).
thf(6,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( lessf @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( lessf @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz45) ).
thf(15,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( lessf @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( lessf @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,plain,
! [A: frac,B: frac] :
( ( lessf @ A @ B )
=> ! [C: frac] :
( ( eq @ A @ C )
=> ! [D: frac] :
( ( eq @ B @ D )
=> ( lessf @ C @ D ) ) ) ),
inference(miniscope,[status(thm)],[15]) ).
thf(17,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ~ ( eq @ A @ C )
| ~ ( eq @ B @ D )
| ( lessf @ C @ D ) ),
inference(cnf,[status(esa)],[16]) ).
thf(34,plain,
! [E: frac,D: frac,C: frac,B: frac,A: frac] :
( ~ ( lessf @ B @ C )
| ~ ( eq @ B @ D )
| ~ $true
| ( lessf @ D @ E )
| ( ( eq @ A @ A )
!= ( eq @ C @ E ) ) ),
inference(paramod_ordered,[status(thm)],[24,17]) ).
thf(35,plain,
! [E: frac,D: frac,C: frac,B: frac,A: frac] :
( ~ ( lessf @ B @ C )
| ~ ( eq @ B @ D )
| ( lessf @ D @ E )
| ( ( eq @ A @ A )
!= ( eq @ C @ E ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(36,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ B @ A )
| ~ ( eq @ B @ C )
| ( lessf @ C @ A ) ),
inference(pattern_uni,[status(thm)],[35:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(46,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ B @ A )
| ~ ( eq @ B @ C )
| ( lessf @ C @ A ) ),
inference(simp,[status(thm)],[36]) ).
thf(514,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ B @ A )
| ~ $true
| ( lessf @ C @ A )
| ( ( eq @ y @ x )
!= ( eq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[265,46]) ).
thf(515,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ B @ A )
| ( lessf @ C @ A )
| ( ( eq @ y @ x )
!= ( eq @ B @ C ) ) ),
inference(simp,[status(thm)],[514]) ).
thf(516,plain,
! [A: frac] :
( ~ ( lessf @ y @ A )
| ( lessf @ x @ A ) ),
inference(pattern_uni,[status(thm)],[515:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( x ))]]) ).
thf(2273,plain,
! [A: frac] :
( ~ $true
| ( lessf @ x @ A )
| ( ( lessf @ y @ z )
!= ( lessf @ y @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13,516]) ).
thf(2274,plain,
! [A: frac] :
( ( lessf @ x @ A )
| ( ( lessf @ y @ z )
!= ( lessf @ y @ A ) ) ),
inference(simp,[status(thm)],[2273]) ).
thf(2275,plain,
lessf @ x @ z,
inference(pattern_uni,[status(thm)],[2274:[bind(A,$thf( z ))]]) ).
thf(2289,plain,
$false,
inference(rewrite,[status(thm)],[2275,10]) ).
thf(2290,plain,
$false,
inference(simp,[status(thm)],[2289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM742^1 : 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
% 0.10/0.21 % Computer : n017.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 12:43:21 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.86/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.98 % [INFO] Parsing done (188ms).
% 1.19/0.99 % [INFO] Running in sequential loop mode.
% 1.79/1.37 % [INFO] eprover registered as external prover.
% 1.79/1.38 % [INFO] Scanning for conjecture ...
% 1.98/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 1.98/1.49 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.14/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.14/1.53 % [INFO] Type checking passed.
% 2.14/1.53 % [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 ...
% 12.19/4.23 % [INFO] Killing All external provers ...
% 12.19/4.23 % Time passed: 3881ms (effective reasoning time: 3228ms)
% 12.19/4.23 % 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)>
% 12.19/4.23 % Axioms used in derivation (6): satz50, satz37, l, satz45, satz38, k
% 12.19/4.23 % No. of inferences in proof: 45
% 12.19/4.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3881 ms resp. 3228 ms w/o parsing
% 12.19/4.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.19/4.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------