%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN166-1 : TPTP v9.3.1. Released v1.1.0.
% 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 : n008.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 09:16:55 AM UTC 2026
% Result : Unsatisfiable 148.96s 90.50s
% Output : Refutation 148.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 61 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 168 ( 14 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 492 ( 82 ~; 79 |; 0 &; 331 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 84 ( 0 ^; 84 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(p1_decl,type,
p1: $i > $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(m0_decl,type,
m0: $i > $i > $i > $o ).
thf(p0_decl,type,
p0: $i > $i > $o ).
thf(c_decl,type,
c: $i ).
thf(m1_decl,type,
m1: $i > $i > $i > $o ).
thf(q0_decl,type,
q0: $i > $i > $o ).
thf(s0_decl,type,
s0: $i > $o ).
thf(k0_decl,type,
k0: $i > $o ).
thf(l0_decl,type,
l0: $i > $o ).
thf(340,axiom,
b @ ( a @ q0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_36) ).
thf(1012,plain,
b @ ( a @ q0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( c @ ( B @ m1 ) ) )
| ~ ( B @ ( A @ q0 ) )
| ~ ( a @ ( C @ ( a @ m0 ) ) )
| ( B @ ( a @ ( A @ m1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_024) ).
thf(1045,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( c @ ( B @ m1 ) ) )
| ~ ( B @ ( A @ q0 ) )
| ~ ( a @ ( C @ ( a @ m0 ) ) )
| ( B @ ( a @ ( A @ m1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(1046,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( c @ ( B @ m1 ) ) )
| ~ ( B @ ( A @ q0 ) )
| ~ ( a @ ( C @ ( a @ m0 ) ) )
| ( B @ ( a @ ( A @ m1 ) ) ) ),
inference(cnf,[status(esa)],[1045]) ).
thf(345,axiom,
! [A: $i] : ( a @ ( A @ ( a @ m0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).
thf(1021,plain,
! [A: $i] : ( a @ ( A @ ( a @ m0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(46147,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( c @ ( B @ m1 ) ) )
| ~ ( B @ ( A @ q0 ) )
| ~ $true
| ( B @ ( a @ ( A @ m1 ) ) ) ),
inference(rewrite,[status(thm)],[1046,1021]) ).
thf(46148,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( c @ ( B @ m1 ) ) )
| ~ ( B @ ( A @ q0 ) )
| ( B @ ( a @ ( A @ m1 ) ) ) ),
inference(simp,[status(thm)],[46147]) ).
thf(46222,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ q0 ) )
!= ( B @ ( A @ q0 ) ) )
| ~ ( B @ ( c @ ( B @ m1 ) ) )
| ~ $true
| ( B @ ( a @ ( A @ m1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1012,46148]) ).
thf(46223,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ q0 ) )
!= ( B @ ( A @ q0 ) ) )
| ~ ( B @ ( c @ ( B @ m1 ) ) )
| ( B @ ( a @ ( A @ m1 ) ) ) ),
inference(simp,[status(thm)],[46222]) ).
thf(46224,plain,
( ~ ( b @ ( c @ ( b @ m1 ) ) )
| ( b @ ( a @ ( a @ m1 ) ) ) ),
inference(pattern_uni,[status(thm)],[46223:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(263,axiom,
! [A: $i] : ( A @ ( b @ p0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).
thf(870,plain,
! [A: $i] : ( A @ ( b @ p0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ~ ( A @ s0 )
| ~ ( B @ ( A @ p0 ) )
| ( A @ ( B @ ( A @ m1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_029) ).
thf(437,plain,
! [B: $i,A: $i] :
( ~ ( A @ s0 )
| ~ ( B @ ( A @ p0 ) )
| ( A @ ( B @ ( A @ m1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(438,plain,
! [B: $i,A: $i] :
( ~ ( A @ s0 )
| ~ ( B @ ( A @ p0 ) )
| ( A @ ( B @ ( A @ m1 ) ) ) ),
inference(cnf,[status(esa)],[437]) ).
thf(3699,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( b @ p0 ) )
!= ( C @ ( B @ p0 ) ) )
| ~ ( B @ s0 )
| ~ $true
| ( B @ ( C @ ( B @ m1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[870,438]) ).
thf(3700,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( b @ p0 ) )
!= ( C @ ( B @ p0 ) ) )
| ~ ( B @ s0 )
| ( B @ ( C @ ( B @ m1 ) ) ) ),
inference(simp,[status(thm)],[3699]) ).
thf(3701,plain,
! [A: $i] :
( ~ ( b @ s0 )
| ( b @ ( A @ ( b @ m1 ) ) ) ),
inference(pattern_uni,[status(thm)],[3700:[bind(A,$thf( A )),bind(B,$thf( b )),bind(C,$thf( A ))]]) ).
thf(253,axiom,
b @ s0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(851,plain,
b @ s0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(3835,plain,
! [A: $i] :
( ~ $true
| ( b @ ( A @ ( b @ m1 ) ) ) ),
inference(rewrite,[status(thm)],[3701,851]) ).
thf(3836,plain,
! [A: $i] : ( b @ ( A @ ( b @ m1 ) ) ),
inference(simp,[status(thm)],[3835]) ).
thf(46602,plain,
( ~ $true
| ( b @ ( a @ ( a @ m1 ) ) ) ),
inference(rewrite,[status(thm)],[46224,3836]) ).
thf(46603,plain,
b @ ( a @ ( a @ m1 ) ),
inference(simp,[status(thm)],[46602]) ).
thf(237,axiom,
b @ k0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_32) ).
thf(826,plain,
b @ k0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(305,axiom,
a @ l0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
thf(949,plain,
a @ l0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ~ ( B @ k0 )
| ~ ( A @ l0 )
| ( A @ ( B @ ( A @ m1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_021) ).
thf(416,plain,
! [B: $i,A: $i] :
( ~ ( B @ k0 )
| ~ ( A @ l0 )
| ( A @ ( B @ ( A @ m1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(417,plain,
! [B: $i,A: $i] :
( ~ ( B @ k0 )
| ~ ( A @ l0 )
| ( A @ ( B @ ( A @ m1 ) ) ) ),
inference(cnf,[status(esa)],[416]) ).
thf(2812,plain,
! [B: $i,A: $i] :
( ( ( a @ l0 )
!= ( A @ l0 ) )
| ~ ( B @ k0 )
| ~ $true
| ( A @ ( B @ ( A @ m1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[949,417]) ).
thf(2813,plain,
! [B: $i,A: $i] :
( ( ( a @ l0 )
!= ( A @ l0 ) )
| ~ ( B @ k0 )
| ( A @ ( B @ ( A @ m1 ) ) ) ),
inference(simp,[status(thm)],[2812]) ).
thf(2814,plain,
! [A: $i] :
( ~ ( A @ k0 )
| ( a @ ( A @ ( a @ m1 ) ) ) ),
inference(pattern_uni,[status(thm)],[2813:[bind(A,$thf( a ))]]) ).
thf(2829,plain,
! [A: $i] :
( ~ ( A @ k0 )
| ( a @ ( A @ ( a @ m1 ) ) ) ),
inference(simp,[status(thm)],[2814]) ).
thf(2892,plain,
! [A: $i] :
( ( ( b @ k0 )
!= ( A @ k0 ) )
| ~ $true
| ( a @ ( A @ ( a @ m1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[826,2829]) ).
thf(2893,plain,
! [A: $i] :
( ( ( b @ k0 )
!= ( A @ k0 ) )
| ( a @ ( A @ ( a @ m1 ) ) ) ),
inference(simp,[status(thm)],[2892]) ).
thf(2894,plain,
a @ ( b @ ( a @ m1 ) ),
inference(pattern_uni,[status(thm)],[2893:[bind(A,$thf( b ))]]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ m1 ) ) )
| ~ ( A @ ( B @ ( C @ m1 ) ) )
| ( B @ ( B @ ( A @ m1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_016) ).
thf(616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ m1 ) ) )
| ~ ( A @ ( B @ ( C @ m1 ) ) )
| ( B @ ( B @ ( A @ m1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ m1 ) ) )
| ~ ( A @ ( B @ ( C @ m1 ) ) )
| ( B @ ( B @ ( A @ m1 ) ) ) ),
inference(cnf,[status(esa)],[616]) ).
thf(14748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( a @ ( b @ ( a @ m1 ) ) )
!= ( A @ ( B @ ( C @ m1 ) ) ) )
| ~ ( B @ ( D @ ( C @ m1 ) ) )
| ~ $true
| ( B @ ( B @ ( A @ m1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2894,617]) ).
thf(14749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( a @ ( b @ ( a @ m1 ) ) )
!= ( A @ ( B @ ( C @ m1 ) ) ) )
| ~ ( B @ ( D @ ( C @ m1 ) ) )
| ( B @ ( B @ ( A @ m1 ) ) ) ),
inference(simp,[status(thm)],[14748]) ).
thf(14750,plain,
! [A: $i] :
( ~ ( b @ ( A @ ( a @ m1 ) ) )
| ( b @ ( b @ ( a @ m1 ) ) ) ),
inference(pattern_uni,[status(thm)],[14749:[bind(A,$thf( a )),bind(B,$thf( b )),bind(C,$thf( a ))]]) ).
thf(14968,plain,
! [A: $i] :
( ~ ( b @ ( A @ ( a @ m1 ) ) )
| ( b @ ( b @ ( a @ m1 ) ) ) ),
inference(simp,[status(thm)],[14750]) ).
thf(49689,plain,
! [A: $i] :
( ( ( b @ ( a @ ( a @ m1 ) ) )
!= ( b @ ( A @ ( a @ m1 ) ) ) )
| ~ $true
| ( b @ ( b @ ( a @ m1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[46603,14968]) ).
thf(49690,plain,
! [A: $i] :
( ( ( b @ ( a @ ( a @ m1 ) ) )
!= ( b @ ( A @ ( a @ m1 ) ) ) )
| ( b @ ( b @ ( a @ m1 ) ) ) ),
inference(simp,[status(thm)],[49689]) ).
thf(49691,plain,
b @ ( b @ ( a @ m1 ) ),
inference(pattern_uni,[status(thm)],[49690:[bind(A,$thf( a ))]]) ).
thf(321,axiom,
! [B: $i,A: $i] :
( ~ ( B @ k0 )
| ~ ( b @ ( B @ ( A @ m1 ) ) )
| ( B @ ( b @ ( A @ p1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_083) ).
thf(977,plain,
! [B: $i,A: $i] :
( ~ ( B @ k0 )
| ~ ( b @ ( B @ ( A @ m1 ) ) )
| ( B @ ( b @ ( A @ p1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(978,plain,
! [B: $i,A: $i] :
( ~ ( B @ k0 )
| ~ ( b @ ( B @ ( A @ m1 ) ) )
| ( B @ ( b @ ( A @ p1 ) ) ) ),
inference(cnf,[status(esa)],[977]) ).
thf(50085,plain,
! [B: $i,A: $i] :
( ( ( b @ ( b @ ( a @ m1 ) ) )
!= ( b @ ( B @ ( A @ m1 ) ) ) )
| ~ ( B @ k0 )
| ~ $true
| ( B @ ( b @ ( A @ p1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[49691,978]) ).
thf(50086,plain,
! [B: $i,A: $i] :
( ( ( b @ ( b @ ( a @ m1 ) ) )
!= ( b @ ( B @ ( A @ m1 ) ) ) )
| ~ ( B @ k0 )
| ( B @ ( b @ ( A @ p1 ) ) ) ),
inference(simp,[status(thm)],[50085]) ).
thf(50087,plain,
( ~ ( b @ k0 )
| ( b @ ( b @ ( a @ p1 ) ) ) ),
inference(pattern_uni,[status(thm)],[50086:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(1,negated_conjecture,
~ ( b @ ( b @ ( a @ p1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(370,plain,
~ ( b @ ( b @ ( a @ p1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(371,plain,
~ ( b @ ( b @ ( a @ p1 ) ) ),
inference(polarity_switch,[status(thm)],[370]) ).
thf(50154,plain,
( ~ $true
| $false ),
inference(rewrite,[status(thm)],[50087,371,826]) ).
thf(50155,plain,
$false,
inference(simp,[status(thm)],[50154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN166-1 : TPTP v9.3.1. Released v1.1.0.
% 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
% 0.13/10.62 % Computer : n008.cluster.edu
% 0.13/10.62 % Model : x86_64 x86_64
% 0.13/10.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.62 % Memory : 8046.5625MB
% 0.13/10.62 % OS : Linux 6.8.0-71-generic
% 0.13/10.62 % CPULimit : 300
% 0.13/10.62 % WCLimit : 300
% 0.13/10.62 % DateTime : Sat Sep 26 17:18:22 UTC 2026
% 0.13/10.62 % CPUTime :
% 0.13/10.62 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
% 1.01/11.21 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.74/11.52 % [INFO] Parsing done (305ms).
% 1.74/11.53 % [INFO] Running in sequential loop mode.
% 2.63/11.94 % [INFO] eprover registered as external prover.
% 2.63/11.95 % [INFO] Scanning for conjecture ...
% 2.93/12.09 % [INFO] Found a conjecture (or negated_conjecture) and 368 axioms. Running axiom selection ...
% 3.44/12.24 % [INFO] Axiom selection finished. Selected 368 axioms (removed 0 axioms).
% 4.07/12.43 % [INFO] Problem is propositional (TPTP CNF).
% 4.07/12.44 % [INFO] Type checking passed.
% 4.07/12.45 % [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 ...
% 148.77/90.49 % [INFO] Killing All external provers ...
% 148.96/90.50 % Time passed: 79716ms (effective reasoning time: 78954ms)
% 148.96/90.50 % Axioms used in derivation (11): axiom_32, rule_016, axiom_20, axiom_36, axiom_5, rule_029, rule_083, axiom_12, axiom_14, rule_021, rule_024
% 148.96/90.50 % No. of inferences in proof: 61
% 148.96/90.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 79716 ms resp. 78954 ms w/o parsing
% 148.96/90.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 148.96/90.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------