%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM756_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.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 : Sun Sep 27 08:09:53 AM UTC 2026
% Result : Theorem 4.54s 2.78s
% Output : Refutation 4.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 116 ( 10 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 412 ( 64 ~; 29 |; 2 &; 292 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 76 ( 0 ^; 76 !; 0 ?; 76 :)
% 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(eq_decl,type,
eq: frac > frac > $o ).
thf(pf_decl,type,
pf: frac > frac > frac ).
thf(lessf_decl,type,
lessf: frac > frac > $o ).
thf(moref_decl,type,
moref: frac > frac > $o ).
thf(7,axiom,
! [A: frac,B: frac] :
( ~ ( B @ ( A @ eq ) )
=> ( ~ ( B @ ( A @ moref ) )
=> ( B @ ( A @ lessf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41a) ).
thf(23,plain,
! [A: frac,B: frac] :
( ~ ( B @ ( A @ eq ) )
=> ( ~ ( B @ ( A @ moref ) )
=> ( B @ ( A @ lessf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,plain,
! [B: frac,A: frac] :
( ( B @ ( A @ lessf ) )
| ( B @ ( A @ moref ) )
| ( B @ ( A @ eq ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(8,axiom,
! [A: frac,B: frac,C: frac] :
( ( B @ ( A @ moref ) )
=> ( C @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62a) ).
thf(25,plain,
! [A: frac,B: frac,C: frac] :
( ( B @ ( A @ moref ) )
=> ( C @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(26,plain,
! [A: frac,B: frac] :
( ( B @ ( A @ moref ) )
=> ! [C: frac] : ( C @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) ) ),
inference(miniscope,[status(thm)],[25]) ).
thf(27,plain,
! [C: frac,B: frac,A: frac] :
( ( C @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) )
| ~ ( B @ ( A @ moref ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(3,axiom,
z @ ( y @ pf ) @ ( z @ ( x @ pf ) @ eq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(10,plain,
z @ ( y @ pf ) @ ( z @ ( x @ pf ) @ eq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: frac,B: frac] :
~ ( ( ( B @ ( A @ eq ) )
=> ~ ( B @ ( A @ moref ) ) )
=> ~ ~ ( ( ( B @ ( A @ moref ) )
=> ~ ( B @ ( A @ lessf ) ) )
=> ~ ( ( B @ ( A @ lessf ) )
=> ~ ( B @ ( A @ eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41b) ).
thf(12,plain,
! [A: frac,B: frac] :
~ ( ( ( B @ ( A @ eq ) )
=> ~ ( B @ ( A @ moref ) ) )
=> ( ( ( B @ ( A @ moref ) )
=> ~ ( B @ ( A @ lessf ) ) )
=> ~ ( ( B @ ( A @ lessf ) )
=> ~ ( B @ ( A @ eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,plain,
~ ( ! [A: frac,B: frac] :
( ( B @ ( A @ eq ) )
=> ~ ( B @ ( A @ moref ) ) )
=> ( ! [A: frac,B: frac] :
( ( B @ ( A @ moref ) )
=> ~ ( B @ ( A @ lessf ) ) )
=> ~ ! [A: frac,B: frac] :
( ( B @ ( A @ lessf ) )
=> ~ ( B @ ( A @ eq ) ) ) ) ),
inference(miniscope,[status(thm)],[12]) ).
thf(14,plain,
! [F: frac,E: frac,D: frac,C: frac,B: frac,A: frac] :
( ( ~ ( F @ ( E @ eq ) )
| ~ ( F @ ( E @ lessf ) ) )
& ( ~ ( D @ ( C @ lessf ) )
| ~ ( D @ ( C @ moref ) ) )
& ( ~ ( B @ ( A @ moref ) )
| ~ ( B @ ( A @ eq ) ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
! [B: frac,A: frac] :
( ~ ( B @ ( A @ moref ) )
| ~ ( B @ ( A @ eq ) ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(31,plain,
! [B: frac,A: frac] :
( ( ( z @ ( y @ pf ) @ ( z @ ( x @ pf ) @ eq ) )
!= ( B @ ( A @ eq ) ) )
| ~ ( B @ ( A @ moref ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10,15]) ).
thf(32,plain,
! [B: frac,A: frac] :
( ( ( z @ ( y @ pf ) @ ( z @ ( x @ pf ) @ eq ) )
!= ( B @ ( A @ eq ) ) )
| ~ ( B @ ( A @ moref ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(33,plain,
~ ( z @ ( y @ pf ) @ ( z @ ( x @ pf ) @ moref ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( z @ ( x @ pf ) )),bind(B,$thf( z @ ( y @ pf ) ))]]) ).
thf(69,plain,
! [C: frac,B: frac,A: frac] :
( ( ( C @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) )
!= ( z @ ( y @ pf ) @ ( z @ ( x @ pf ) @ moref ) ) )
| ~ $true
| ~ ( B @ ( A @ moref ) ) ),
inference(paramod_ordered,[status(thm)],[27,33]) ).
thf(70,plain,
! [C: frac,B: frac,A: frac] :
( ( ( C @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) )
!= ( z @ ( y @ pf ) @ ( z @ ( x @ pf ) @ moref ) ) )
| ~ ( B @ ( A @ moref ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(71,plain,
~ ( y @ ( x @ moref ) ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
thf(85,plain,
! [B: frac,A: frac] :
( ( ( B @ ( A @ moref ) )
!= ( y @ ( x @ moref ) ) )
| ~ $true
| ( B @ ( A @ lessf ) )
| ( B @ ( A @ eq ) ) ),
inference(paramod_ordered,[status(thm)],[24,71]) ).
thf(86,plain,
! [B: frac,A: frac] :
( ( ( B @ ( A @ moref ) )
!= ( y @ ( x @ moref ) ) )
| ( B @ ( A @ lessf ) )
| ( B @ ( A @ eq ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(87,plain,
( ( y @ ( x @ lessf ) )
| ( y @ ( x @ eq ) ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(6,axiom,
! [A: frac,B: frac,C: frac] :
( ( B @ ( A @ lessf ) )
=> ( C @ ( B @ pf ) @ ( C @ ( A @ pf ) @ lessf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62c) ).
thf(20,plain,
! [A: frac,B: frac,C: frac] :
( ( B @ ( A @ lessf ) )
=> ( C @ ( B @ pf ) @ ( C @ ( A @ pf ) @ lessf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,plain,
! [A: frac,B: frac] :
( ( B @ ( A @ lessf ) )
=> ! [C: frac] : ( C @ ( B @ pf ) @ ( C @ ( A @ pf ) @ lessf ) ) ),
inference(miniscope,[status(thm)],[20]) ).
thf(22,plain,
! [C: frac,B: frac,A: frac] :
( ( C @ ( B @ pf ) @ ( C @ ( A @ pf ) @ lessf ) )
| ~ ( B @ ( A @ lessf ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(17,plain,
! [B: frac,A: frac] :
( ~ ( B @ ( A @ eq ) )
| ~ ( B @ ( A @ lessf ) ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(19,plain,
! [B: frac,A: frac] :
( ~ ( B @ ( A @ eq ) )
| ~ ( B @ ( A @ lessf ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(43,plain,
! [B: frac,A: frac] :
( ( ( z @ ( y @ pf ) @ ( z @ ( x @ pf ) @ eq ) )
!= ( B @ ( A @ eq ) ) )
| ~ $true
| ~ ( B @ ( A @ lessf ) ) ),
inference(paramod_ordered,[status(thm)],[10,19]) ).
thf(44,plain,
! [B: frac,A: frac] :
( ( ( z @ ( y @ pf ) @ ( z @ ( x @ pf ) @ eq ) )
!= ( B @ ( A @ eq ) ) )
| ~ ( B @ ( A @ lessf ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(45,plain,
~ ( z @ ( y @ pf ) @ ( z @ ( x @ pf ) @ lessf ) ),
inference(pattern_uni,[status(thm)],[44:[bind(A,$thf( z @ ( x @ pf ) )),bind(B,$thf( z @ ( y @ pf ) ))]]) ).
thf(46,plain,
! [C: frac,B: frac,A: frac] :
( ( ( C @ ( B @ pf ) @ ( C @ ( A @ pf ) @ lessf ) )
!= ( z @ ( y @ pf ) @ ( z @ ( x @ pf ) @ lessf ) ) )
| ~ $true
| ~ ( B @ ( A @ lessf ) ) ),
inference(paramod_ordered,[status(thm)],[22,45]) ).
thf(47,plain,
! [C: frac,B: frac,A: frac] :
( ( ( C @ ( B @ pf ) @ ( C @ ( A @ pf ) @ lessf ) )
!= ( z @ ( y @ pf ) @ ( z @ ( x @ pf ) @ lessf ) ) )
| ~ ( B @ ( A @ lessf ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(48,plain,
~ ( y @ ( x @ lessf ) ),
inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
thf(1,conjecture,
y @ ( x @ eq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz63b) ).
thf(2,negated_conjecture,
~ ( y @ ( x @ eq ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ( y @ ( x @ eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(109,plain,
( $false
| $false ),
inference(rewrite,[status(thm)],[87,48,9]) ).
thf(110,plain,
$false,
inference(simp,[status(thm)],[109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM756_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.42 % Computer : n014.cluster.edu
% 0.13/0.42 % Model : x86_64 x86_64
% 0.13/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.42 % Memory : 8046.5625MB
% 0.13/0.42 % OS : Linux 6.8.0-71-generic
% 0.13/0.42 % CPULimit : 300
% 0.13/0.42 % WCLimit : 300
% 0.13/0.42 % DateTime : Sat Sep 26 04:00:03 UTC 2026
% 0.13/0.42 % CPUTime :
% 0.13/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.82/1.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/1.20 % [INFO] Parsing done (180ms).
% 1.33/1.21 % [INFO] Running in sequential loop mode.
% 1.96/1.61 % [INFO] eprover registered as external prover.
% 1.96/1.62 % [INFO] Scanning for conjecture ...
% 2.15/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.15/1.74 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.15/1.78 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.15/1.78 % [INFO] Type checking passed.
% 2.15/1.79 % [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 ...
% 4.54/2.77 % [INFO] Killing All external provers ...
% 4.54/2.78 % Time passed: 2203ms (effective reasoning time: 1556ms)
% 4.54/2.78 % 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)>
% 4.54/2.78 % Axioms used in derivation (5): e, satz41b, satz62a, satz62c, satz41a
% 4.54/2.78 % No. of inferences in proof: 40
% 4.54/2.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2203 ms resp. 1556 ms w/o parsing
% 4.91/2.84 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.91/2.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------