%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM765^1 : 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 : 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 6.11s 2.07s
% Output : Refutation 6.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 190 ( 16 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 690 ( 95 ~; 67 |; 3 &; 494 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 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 : 92 ( 0 ^; 92 !; 0 ?; 92 :)
% 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(8,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( ~ ( moref @ A @ B )
=> ( eq @ A @ B ) )
=> ( ( moref @ C @ D )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz65a) ).
thf(26,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( ~ ( moref @ A @ B )
=> ( eq @ A @ B ) )
=> ( ( moref @ C @ D )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
! [A: frac,B: frac] :
( ( ~ ( moref @ A @ B )
=> ( eq @ A @ B ) )
=> ! [C: frac,D: frac] :
( ( moref @ C @ D )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[26]) ).
thf(28,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ( ~ ( moref @ A @ B )
| ~ ( moref @ C @ D )
| ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) )
& ( ~ ( eq @ A @ B )
| ~ ( moref @ C @ D )
| ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(30,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( moref @ C @ D )
| ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(1,conjecture,
( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz66) ).
thf(2,negated_conjecture,
~ ( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
& ~ ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(408,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( moref @ C @ D )
| ~ $true
| ( ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,11]) ).
thf(409,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( moref @ C @ D )
| ( ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(simp,[status(thm)],[408]) ).
thf(410,plain,
( ~ ( eq @ x @ y )
| ~ ( moref @ z @ u ) ),
inference(pattern_uni,[status(thm)],[409:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(3,axiom,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(13,plain,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
( ( moref @ x @ y )
| ( eq @ x @ y ) ),
inference(cnf,[status(esa)],[13]) ).
thf(4,axiom,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(15,plain,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
( ( moref @ z @ u )
| ( eq @ z @ u ) ),
inference(cnf,[status(esa)],[15]) ).
thf(7,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( ~ ( moref @ C @ D )
=> ( eq @ C @ D ) )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz65b) ).
thf(21,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( ~ ( moref @ C @ D )
=> ( eq @ C @ D ) )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,plain,
! [A: frac,B: frac] :
( ( moref @ A @ B )
=> ! [C: frac,D: frac] :
( ( ~ ( moref @ C @ D )
=> ( eq @ C @ D ) )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(23,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ( ~ ( moref @ A @ B )
| ~ ( moref @ C @ D )
| ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) )
& ( ~ ( moref @ A @ B )
| ~ ( eq @ C @ D )
| ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(25,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ C @ D )
| ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(226,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ C @ D )
| ~ $true
| ( ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,11]) ).
thf(227,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ C @ D )
| ( ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(simp,[status(thm)],[226]) ).
thf(228,plain,
( ~ ( moref @ x @ y )
| ~ ( eq @ z @ u ) ),
inference(pattern_uni,[status(thm)],[227:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(272,plain,
( ( moref @ z @ u )
| ~ ( moref @ x @ y )
| ~ $true
| ( ( eq @ z @ u )
!= ( eq @ z @ u ) ) ),
inference(paramod_ordered,[status(thm)],[16,228]) ).
thf(273,plain,
( ( moref @ z @ u )
| ~ ( moref @ x @ y )
| ( ( eq @ z @ u )
!= ( eq @ z @ u ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(274,plain,
( ( moref @ z @ u )
| ~ ( moref @ x @ y ) ),
inference(pattern_uni,[status(thm)],[273:[]]) ).
thf(24,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( moref @ C @ D )
| ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(98,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( moref @ C @ D )
| ~ $true
| ( ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,11]) ).
thf(99,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( moref @ C @ D )
| ( ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
( ~ ( moref @ x @ y )
| ~ ( moref @ z @ u ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(287,plain,
( ~ ( moref @ x @ y )
| ~ ( moref @ x @ y )
| ~ $true
| ( ( moref @ z @ u )
!= ( moref @ z @ u ) ) ),
inference(paramod_ordered,[status(thm)],[274,100]) ).
thf(288,plain,
( ~ ( moref @ x @ y )
| ( ( moref @ z @ u )
!= ( moref @ z @ u ) ) ),
inference(simp,[status(thm)],[287]) ).
thf(289,plain,
~ ( moref @ x @ y ),
inference(pattern_uni,[status(thm)],[288:[]]) ).
thf(314,plain,
( $false
| ( eq @ x @ y ) ),
inference(rewrite,[status(thm)],[14,289]) ).
thf(315,plain,
eq @ x @ y,
inference(simp,[status(thm)],[314]) ).
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(18,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(19,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)],[18]) ).
thf(20,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)],[19]) ).
thf(12,plain,
~ ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(49,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ C @ D )
| ~ $true
| ( ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,12]) ).
thf(50,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ C @ D )
| ( ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(51,plain,
( ~ ( eq @ x @ y )
| ~ ( eq @ z @ u ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(62,plain,
( ( moref @ x @ y )
| ~ $true
| ~ ( eq @ z @ u )
| ( ( eq @ x @ y )
!= ( eq @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[14,51]) ).
thf(63,plain,
( ( moref @ x @ y )
| ~ ( eq @ z @ u )
| ( ( eq @ x @ y )
!= ( eq @ x @ y ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(64,plain,
( ( moref @ x @ y )
| ~ ( eq @ z @ u ) ),
inference(pattern_uni,[status(thm)],[63:[]]) ).
thf(87,plain,
( ( moref @ z @ u )
| ( moref @ x @ y )
| ~ $true
| ( ( eq @ z @ u )
!= ( eq @ z @ u ) ) ),
inference(paramod_ordered,[status(thm)],[16,64]) ).
thf(88,plain,
( ( moref @ z @ u )
| ( moref @ x @ y )
| ( ( eq @ z @ u )
!= ( eq @ z @ u ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(89,plain,
( ( moref @ z @ u )
| ( moref @ x @ y ) ),
inference(pattern_uni,[status(thm)],[88:[]]) ).
thf(316,plain,
( ( moref @ z @ u )
| $false ),
inference(rewrite,[status(thm)],[89,289]) ).
thf(317,plain,
moref @ z @ u,
inference(simp,[status(thm)],[316]) ).
thf(447,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[410,315,317]) ).
thf(448,plain,
$false,
inference(simp,[status(thm)],[447]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM765^1 : 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
% 0.11/0.21 % Computer : n019.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 12:53:47 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.68/0.52 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.90/0.63 % [INFO] Parsing done (100ms).
% 0.90/0.63 % [INFO] Running in sequential loop mode.
% 1.37/0.83 % [INFO] eprover registered as external prover.
% 1.37/0.83 % [INFO] Scanning for conjecture ...
% 1.37/0.87 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 1.37/0.89 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.62/0.91 % [INFO] Problem is higher-order (TPTP THF).
% 1.62/0.91 % [INFO] Type checking passed.
% 1.62/0.91 % [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 ...
% 6.11/2.06 % [INFO] Killing All external provers ...
% 6.11/2.06 % Time passed: 1766ms (effective reasoning time: 1424ms)
% 6.11/2.06 % 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)>
% 6.11/2.07 % Axioms used in derivation (5): satz65b, n, m, satz65a, satz56
% 6.11/2.07 % No. of inferences in proof: 57
% 6.11/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1766 ms resp. 1424 ms w/o parsing
% 6.11/2.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.11/2.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------