%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM743^1 : 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 : n007.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 5.41s 2.89s
% Output : Refutation 5.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 119 ( 10 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 308 ( 48 ~; 41 |; 0 &; 202 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 63 ( 0 ^; 63 !; 0 ?; 63 :)
% 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(3,axiom,
lessf @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(10,plain,
lessf @ x @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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(19,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(20,plain,
! [A: frac,B: frac] :
( ( lessf @ A @ B )
=> ! [C: frac] :
( ( lessf @ B @ C )
=> ( lessf @ A @ C ) ) ),
inference(miniscope,[status(thm)],[19]) ).
thf(21,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ~ ( lessf @ B @ C )
| ( lessf @ A @ C ) ),
inference(cnf,[status(esa)],[20]) ).
thf(1,conjecture,
lessf @ x @ z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz51b) ).
thf(2,negated_conjecture,
~ ( lessf @ x @ z ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ( lessf @ x @ z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(176,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ~ ( lessf @ B @ C )
| ~ $true
| ( ( lessf @ A @ C )
!= ( lessf @ x @ z ) ) ),
inference(paramod_ordered,[status(thm)],[21,9]) ).
thf(177,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ~ ( lessf @ B @ C )
| ( ( lessf @ A @ C )
!= ( lessf @ x @ z ) ) ),
inference(simp,[status(thm)],[176]) ).
thf(178,plain,
! [A: frac] :
( ~ ( lessf @ x @ A )
| ~ ( lessf @ A @ z ) ),
inference(pattern_uni,[status(thm)],[177:[bind(A,$thf( x )),bind(B,$thf( B )),bind(C,$thf( z ))]]) ).
thf(204,plain,
! [A: frac] :
( ~ ( lessf @ x @ A )
| ~ ( lessf @ A @ z ) ),
inference(simp,[status(thm)],[178]) ).
thf(272,plain,
! [A: frac] :
( ~ $true
| ~ ( lessf @ A @ z )
| ( ( lessf @ x @ y )
!= ( lessf @ x @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,204]) ).
thf(273,plain,
! [A: frac] :
( ~ ( lessf @ A @ z )
| ( ( lessf @ x @ y )
!= ( lessf @ x @ A ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(274,plain,
~ ( lessf @ y @ z ),
inference(pattern_uni,[status(thm)],[273:[bind(A,$thf( y ))]]) ).
thf(4,axiom,
( ~ ( lessf @ y @ z )
=> ( eq @ y @ z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
thf(11,plain,
( ~ ( lessf @ y @ z )
=> ( eq @ y @ z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
( ( lessf @ y @ z )
| ( eq @ y @ z ) ),
inference(cnf,[status(esa)],[11]) ).
thf(7,axiom,
! [A: frac] : ( eq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz37) ).
thf(17,plain,
! [A: frac] : ( eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,plain,
! [A: frac] : ( eq @ A @ A ),
inference(cnf,[status(esa)],[17]) ).
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(14,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(15,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)],[14]) ).
thf(16,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)],[15]) ).
thf(26,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ $true
| ~ ( eq @ A @ C )
| ~ ( eq @ B @ D )
| ( lessf @ C @ D )
| ( ( lessf @ x @ y )
!= ( lessf @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10,16]) ).
thf(27,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ C )
| ~ ( eq @ B @ D )
| ( lessf @ C @ D )
| ( ( lessf @ x @ y )
!= ( lessf @ A @ B ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(28,plain,
! [B: frac,A: frac] :
( ~ ( eq @ x @ A )
| ~ ( eq @ y @ B )
| ( lessf @ A @ B ) ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(46,plain,
! [B: frac,A: frac] :
( ~ ( eq @ x @ A )
| ~ ( eq @ y @ B )
| ( lessf @ A @ B ) ),
inference(simp,[status(thm)],[28]) ).
thf(133,plain,
! [C: frac,B: frac,A: frac] :
( ~ $true
| ~ ( eq @ y @ C )
| ( lessf @ B @ C )
| ( ( eq @ A @ A )
!= ( eq @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[18,46]) ).
thf(134,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ y @ C )
| ( lessf @ B @ C )
| ( ( eq @ A @ A )
!= ( eq @ x @ B ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(135,plain,
! [A: frac] :
( ~ ( eq @ y @ A )
| ( lessf @ x @ A ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( x )),bind(B,$thf( x ))]]) ).
thf(148,plain,
! [A: frac] :
( ~ ( eq @ y @ A )
| ( lessf @ x @ A ) ),
inference(simp,[status(thm)],[135]) ).
thf(152,plain,
! [A: frac] :
( ( lessf @ y @ z )
| ~ $true
| ( lessf @ x @ A )
| ( ( eq @ y @ z )
!= ( eq @ y @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12,148]) ).
thf(153,plain,
! [A: frac] :
( ( lessf @ y @ z )
| ( lessf @ x @ A )
| ( ( eq @ y @ z )
!= ( eq @ y @ A ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(154,plain,
( ( lessf @ y @ z )
| ( lessf @ x @ z ) ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( z ))]]) ).
thf(208,plain,
( ( lessf @ y @ z )
| $false ),
inference(rewrite,[status(thm)],[154,9]) ).
thf(209,plain,
lessf @ y @ z,
inference(simp,[status(thm)],[208]) ).
thf(317,plain,
~ $true,
inference(rewrite,[status(thm)],[274,209]) ).
thf(318,plain,
$false,
inference(simp,[status(thm)],[317]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM743^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % 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
% 0.10/0.23 % Computer : n007.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 12:45:55 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 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
% 0.96/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.14/0.99 % [INFO] Parsing done (185ms).
% 1.14/1.00 % [INFO] Running in sequential loop mode.
% 1.71/1.39 % [INFO] eprover registered as external prover.
% 1.88/1.40 % [INFO] Scanning for conjecture ...
% 1.88/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.05/1.51 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.05/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.05/1.54 % [INFO] Type checking passed.
% 2.05/1.55 % [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 ...
% 5.41/2.88 % [INFO] Killing All external provers ...
% 5.41/2.89 % Time passed: 2515ms (effective reasoning time: 1873ms)
% 5.41/2.89 % 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)>
% 5.41/2.89 % Axioms used in derivation (5): satz50, satz37, l, satz45, k
% 5.41/2.89 % No. of inferences in proof: 41
% 5.41/2.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2515 ms resp. 1873 ms w/o parsing
% 5.79/2.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.79/2.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------