%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM762^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n019.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 08:18:08 AM UTC 2026
% Result : Theorem 10.04s 3.66s
% Output : Refutation 10.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 149 ( 12 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 547 ( 67 ~; 46 |; 0 &; 408 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 109 ( 0 ^; 109 !; 0 ?; 109 :)
% 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(u_decl,type,
u: frac ).
thf(moref_decl,type,
moref: frac > frac > $o ).
thf(eq_decl,type,
eq: frac > frac > $o ).
thf(pf_decl,type,
pf: frac > frac > frac ).
thf(10,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( moref @ C @ D )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz64) ).
thf(27,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( moref @ C @ D )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(28,plain,
! [A: frac,B: frac] :
( ( moref @ A @ B )
=> ! [C: frac,D: frac] :
( ( moref @ C @ D )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[27]) ).
thf(29,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( moref @ C @ D )
| ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(1,conjecture,
moref @ ( pf @ x @ z ) @ ( pf @ y @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz65b) ).
thf(2,negated_conjecture,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(481,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( moref @ C @ D )
| ~ $true
| ( ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,11]) ).
thf(482,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( moref @ C @ D )
| ( ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(simp,[status(thm)],[481]) ).
thf(483,plain,
( ~ ( moref @ x @ y )
| ~ ( moref @ z @ u ) ),
inference(pattern_uni,[status(thm)],[482:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(4,axiom,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(13,plain,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
( ( moref @ z @ u )
| ( eq @ z @ u ) ),
inference(cnf,[status(esa)],[13]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',satz56) ).
thf(24,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)],[9]) ).
thf(25,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ! [C: frac,D: frac] :
( ( eq @ C @ D )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[24]) ).
thf(26,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ C @ D )
| ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(3,axiom,
moref @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(12,plain,
moref @ x @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: frac,B: frac,C: frac] :
( ( moref @ A @ B )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz61) ).
thf(19,plain,
! [A: frac,B: frac,C: frac] :
( ( moref @ A @ B )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,plain,
! [A: frac,B: frac] :
( ( moref @ A @ B )
=> ! [C: frac] : ( moref @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
inference(miniscope,[status(thm)],[19]) ).
thf(21,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ( moref @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(123,plain,
! [C: frac,B: frac,A: frac] :
( ~ $true
| ( moref @ ( pf @ A @ C ) @ ( pf @ B @ C ) )
| ( ( moref @ x @ y )
!= ( moref @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,21]) ).
thf(124,plain,
! [C: frac,B: frac,A: frac] :
( ( moref @ ( pf @ A @ C ) @ ( pf @ B @ C ) )
| ( ( moref @ x @ y )
!= ( moref @ A @ B ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(125,plain,
! [A: frac] : ( moref @ ( pf @ x @ A ) @ ( pf @ y @ A ) ),
inference(pattern_uni,[status(thm)],[124:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(144,plain,
! [A: frac] : ( moref @ ( pf @ x @ A ) @ ( pf @ y @ A ) ),
inference(simp,[status(thm)],[125]) ).
thf(8,axiom,
! [A: frac] : ( eq @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37) ).
thf(22,plain,
! [A: frac] : ( eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(23,plain,
! [A: frac] : ( eq @ A @ A ),
inference(cnf,[status(esa)],[22]) ).
thf(6,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz44) ).
thf(16,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,plain,
! [A: frac,B: frac] :
( ( moref @ A @ B )
=> ! [C: frac] :
( ( eq @ A @ C )
=> ! [D: frac] :
( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
inference(miniscope,[status(thm)],[16]) ).
thf(18,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ A @ C )
| ~ ( eq @ B @ D )
| ( moref @ C @ D ) ),
inference(cnf,[status(esa)],[17]) ).
thf(45,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ A @ C )
| ~ ( eq @ B @ D )
| ~ $true
| ( ( moref @ C @ D )
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,11]) ).
thf(46,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ A @ C )
| ~ ( eq @ B @ D )
| ( ( moref @ C @ D )
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(47,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ A @ ( pf @ x @ z ) )
| ~ ( eq @ B @ ( pf @ y @ u ) ) ),
inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( pf @ x @ z )),bind(D,$thf( pf @ y @ u ))]]) ).
thf(85,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( moref @ B @ C )
| ~ $true
| ~ ( eq @ C @ ( pf @ y @ u ) )
| ( ( eq @ A @ A )
!= ( eq @ B @ ( pf @ x @ z ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,47]) ).
thf(86,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( moref @ B @ C )
| ~ ( eq @ C @ ( pf @ y @ u ) )
| ( ( eq @ A @ A )
!= ( eq @ B @ ( pf @ x @ z ) ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(87,plain,
! [A: frac] :
( ~ ( moref @ ( pf @ x @ z ) @ A )
| ~ ( eq @ A @ ( pf @ y @ u ) ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( pf @ x @ z )),bind(B,$thf( pf @ x @ z )),bind(C,$thf( C ))]]) ).
thf(96,plain,
! [A: frac] :
( ~ ( moref @ ( pf @ x @ z ) @ A )
| ~ ( eq @ A @ ( pf @ y @ u ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(275,plain,
! [B: frac,A: frac] :
( ~ $true
| ~ ( eq @ B @ ( pf @ y @ u ) )
| ( ( moref @ ( pf @ x @ A ) @ ( pf @ y @ A ) )
!= ( moref @ ( pf @ x @ z ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[144,96]) ).
thf(276,plain,
! [B: frac,A: frac] :
( ~ ( eq @ B @ ( pf @ y @ u ) )
| ( ( moref @ ( pf @ x @ A ) @ ( pf @ y @ A ) )
!= ( moref @ ( pf @ x @ z ) @ B ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(277,plain,
~ ( eq @ ( pf @ y @ z ) @ ( pf @ y @ u ) ),
inference(pattern_uni,[status(thm)],[276:[bind(A,$thf( z )),bind(B,$thf( pf @ y @ z ))]]) ).
thf(343,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ C @ D )
| ~ $true
| ( ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( eq @ ( pf @ y @ z ) @ ( pf @ y @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,277]) ).
thf(344,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ C @ D )
| ( ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( eq @ ( pf @ y @ z ) @ ( pf @ y @ u ) ) ) ),
inference(simp,[status(thm)],[343]) ).
thf(345,plain,
( ~ ( eq @ y @ y )
| ~ ( eq @ z @ u ) ),
inference(pattern_uni,[status(thm)],[344:[bind(A,$thf( y )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(408,plain,
( ~ $true
| ~ ( eq @ z @ u ) ),
inference(rewrite,[status(thm)],[345,23]) ).
thf(409,plain,
~ ( eq @ z @ u ),
inference(simp,[status(thm)],[408]) ).
thf(410,plain,
( ( moref @ z @ u )
| $false ),
inference(rewrite,[status(thm)],[14,409]) ).
thf(411,plain,
moref @ z @ u,
inference(simp,[status(thm)],[410]) ).
thf(674,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[483,411,12]) ).
thf(675,plain,
$false,
inference(simp,[status(thm)],[674]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM762^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.10/0.20 % Computer : n019.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 12:53:18 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.87/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.98 % [INFO] Parsing done (200ms).
% 1.22/1.00 % [INFO] Running in sequential loop mode.
% 2.07/1.40 % [INFO] eprover registered as external prover.
% 2.07/1.41 % [INFO] Scanning for conjecture ...
% 2.07/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.24/1.53 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.24/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.57 % [INFO] Type checking passed.
% 2.24/1.57 % [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 ...
% 10.04/3.65 % [INFO] Killing All external provers ...
% 10.04/3.65 % Time passed: 3316ms (effective reasoning time: 2649ms)
% 10.04/3.65 % 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)>
% 10.04/3.66 % Axioms used in derivation (7): n, m, satz37, satz61, satz44, satz64, satz56
% 10.04/3.66 % No. of inferences in proof: 53
% 10.04/3.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3316 ms resp. 2649 ms w/o parsing
% 10.04/3.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.04/3.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------