%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS116+1 : TPTP v9.3.1. Released v3.1.0.
% 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 : n015.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 07:44:41 AM UTC 2026
% Result : Unsatisfiable 4.98s 2.71s
% Output : Refutation 4.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 18
% Syntax : Number of formulae : 37 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 152 ( 0 equ; 0 cnn)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 342 ( 8 ~; 0 |; 46 &; 219 @)
% ( 13 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 22 usr; 2 con; 0-2 aty)
% Number of variables : 88 ( 0 ^; 68 !; 20 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(cowlThing_decl,type,
cowlThing: $i > $o ).
thf(cowlNothing_decl,type,
cowlNothing: $i > $o ).
thf(xsd_string_decl,type,
xsd_string: $i > $o ).
thf(xsd_integer_decl,type,
xsd_integer: $i > $o ).
thf(cUnsatisfiable_decl,type,
cUnsatisfiable: $i > $o ).
thf(ca_decl,type,
ca: $i > $o ).
thf(rs_decl,type,
rs: $i > $i > $o ).
thf(ca_Ax2_decl,type,
ca_Ax2: $i > $o ).
thf(ra_Px1_decl,type,
ra_Px1: $i > $i > $o ).
thf(caxcomp_decl,type,
caxcomp: $i > $o ).
thf(cc_decl,type,
cc: $i > $o ).
thf(rinvR_decl,type,
rinvR: $i > $i > $o ).
thf(ca_Vx7_decl,type,
ca_Vx7: $i > $o ).
thf(rp_decl,type,
rp: $i > $i > $o ).
thf(ca_Vx3_decl,type,
ca_Vx3: $i > $o ).
thf(ca_Vx5_decl,type,
ca_Vx5: $i > $o ).
thf(rr_decl,type,
rr: $i > $i > $o ).
thf(ca_Vx4_decl,type,
ca_Vx4: $i > $o ).
thf(ca_Vx6_decl,type,
ca_Vx6: $i > $o ).
thf(rinvS_decl,type,
rinvS: $i > $i > $o ).
thf(rinvP_decl,type,
rinvP: $i > $i > $o ).
thf(i2003_11_14_17_21_33997_decl,type,
i2003_11_14_17_21_33997: $i ).
thf(11,axiom,
! [A: $i] :
( ( A @ ca_Vx5 )
<=> ! [B: $i] :
( ( B @ ( A @ rr ) )
=> ( B @ cc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(101,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ( A @ rr ) )
=> ( B @ cc ) )
=> ( A @ ca_Vx5 ) )
& ( ( A @ ca_Vx5 )
=> ! [B: $i] :
( ( B @ ( A @ rr ) )
=> ( B @ cc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rinvP ) )
<=> ( A @ ( B @ rp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).
thf(125,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ rp ) )
=> ( B @ ( A @ rinvP ) ) )
& ( ( B @ ( A @ rinvP ) )
=> ( A @ ( B @ rp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ca_Ax2 )
<=> ( ! [B: $i] :
( ( B @ ( A @ rp ) )
=> ( B @ ca_Vx4 ) )
& ? [B: $i] :
( ( B @ cowlThing )
& ( B @ ( A @ rp ) ) )
& ? [B: $i] :
( ( B @ cowlThing )
& ( B @ ( A @ rr ) ) )
& ! [B: $i] :
( ( B @ ( A @ rr ) )
=> ( B @ cc ) )
& ! [B: $i] :
( ( B @ ( A @ rp ) )
=> ( B @ ca_Vx5 ) )
& ! [B: $i] :
( ( B @ ( A @ rp ) )
=> ( B @ ca_Vx3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(57,plain,
! [A: $i] :
( ( ( ! [B: $i] :
( ( B @ ( A @ rp ) )
=> ( B @ ca_Vx4 ) )
& ? [B: $i] :
( ( B @ cowlThing )
& ( B @ ( A @ rp ) ) )
& ? [B: $i] :
( ( B @ cowlThing )
& ( B @ ( A @ rr ) ) )
& ! [B: $i] :
( ( B @ ( A @ rr ) )
=> ( B @ cc ) )
& ! [B: $i] :
( ( B @ ( A @ rp ) )
=> ( B @ ca_Vx5 ) )
& ! [B: $i] :
( ( B @ ( A @ rp ) )
=> ( B @ ca_Vx3 ) ) )
=> ( A @ ca_Ax2 ) )
& ( ( A @ ca_Ax2 )
=> ( ! [B: $i] :
( ( B @ ( A @ rp ) )
=> ( B @ ca_Vx4 ) )
& ? [B: $i] :
( ( B @ cowlThing )
& ( B @ ( A @ rp ) ) )
& ? [B: $i] :
( ( B @ cowlThing )
& ( B @ ( A @ rr ) ) )
& ! [B: $i] :
( ( B @ ( A @ rr ) )
=> ( B @ cc ) )
& ! [B: $i] :
( ( B @ ( A @ rp ) )
=> ( B @ ca_Vx5 ) )
& ! [B: $i] :
( ( B @ ( A @ rp ) )
=> ( B @ ca_Vx3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ca_Vx7 )
<=> ! [B: $i] :
( ( B @ ( A @ rinvP ) )
=> ( B @ ca_Vx6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).
thf(117,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ( A @ rinvP ) )
=> ( B @ ca_Vx6 ) )
=> ( A @ ca_Vx7 ) )
& ( ( A @ ca_Vx7 )
=> ! [B: $i] :
( ( B @ ( A @ rinvP ) )
=> ( B @ ca_Vx6 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ca_Vx6 )
<=> ! [B: $i] :
( ( B @ ( A @ rinvS ) )
=> ( B @ caxcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(109,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ( A @ rinvS ) )
=> ( B @ caxcomp ) )
=> ( A @ ca_Vx6 ) )
& ( ( A @ ca_Vx6 )
=> ! [B: $i] :
( ( B @ ( A @ rinvS ) )
=> ( B @ caxcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ cc )
<=> ! [B: $i] :
( ( B @ ( A @ rinvR ) )
=> ( B @ ca_Vx7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(49,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ( A @ rinvR ) )
=> ( B @ ca_Vx7 ) )
=> ( A @ cc ) )
& ( ( A @ cc )
=> ! [B: $i] :
( ( B @ ( A @ rinvR ) )
=> ( B @ ca_Vx7 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,axiom,
i2003_11_14_17_21_33997 @ cUnsatisfiable,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).
thf(145,plain,
i2003_11_14_17_21_33997 @ cUnsatisfiable,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ cUnsatisfiable )
=> ( A @ ca ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(31,plain,
! [A: $i] :
( ( A @ cUnsatisfiable )
=> ( A @ ca ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ca_Vx3 )
<=> ? [B: $i] :
( ( B @ cowlThing )
& ( B @ ( A @ rr ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
thf(87,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cowlThing )
& ( B @ ( A @ rr ) ) )
=> ( A @ ca_Vx3 ) )
& ( ( A @ ca_Vx3 )
=> ? [B: $i] :
( ( B @ cowlThing )
& ( B @ ( A @ rr ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
thf(19,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ca_Vx4 )
<=> ? [B: $i] :
( ( B @ cowlThing )
& ( B @ ( A @ rp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
thf(94,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cowlThing )
& ( B @ ( A @ rp ) ) )
=> ( A @ ca_Vx4 ) )
& ( ( A @ ca_Vx4 )
=> ? [B: $i] :
( ( B @ cowlThing )
& ( B @ ( A @ rp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rinvR ) )
<=> ( A @ ( B @ rr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).
thf(131,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ rr ) )
=> ( B @ ( A @ rinvR ) ) )
& ( ( B @ ( A @ rinvR ) )
=> ( A @ ( B @ rr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ca )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(37,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) )
=> ( A @ ca ) )
& ( ( A @ ca )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(25,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rinvS ) )
<=> ( A @ ( B @ rs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).
thf(137,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ rs ) )
=> ( B @ ( A @ rinvS ) ) )
& ( ( B @ ( A @ rinvS ) )
=> ( A @ ( B @ rs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ cUnsatisfiable )
=> ? [B: $i] :
( ( B @ ca_Ax2 )
& ( B @ ( A @ rs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(33,plain,
! [A: $i] :
( ( A @ cUnsatisfiable )
=> ? [B: $i] :
( ( B @ ca_Ax2 )
& ( B @ ( A @ rs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ rp ) )
& ( B @ ( A @ rp ) ) )
=> ( C @ ( A @ rp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_16) ).
thf(143,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ rp ) )
& ( B @ ( A @ rp ) ) )
=> ( C @ ( A @ rp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ caxcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(43,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px1 ) )
=> ( A @ caxcomp ) )
& ( ( A @ caxcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(146,plain,
$false,
inference(e,[status(thm)],[101,125,57,117,109,49,145,31,87,19,94,131,37,25,137,33,143,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS116+1 : TPTP v9.3.1. Released v3.1.0.
% 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
% 0.13/0.40 % Computer : n015.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 19:43:27 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.89/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.50/1.20 % [INFO] Parsing done (203ms).
% 1.50/1.21 % [INFO] Running in sequential loop mode.
% 2.20/1.63 % [INFO] eprover registered as external prover.
% 2.20/1.63 % [INFO] Scanning for conjecture ...
% 2.20/1.68 % [INFO] 18 axioms and no conjecture found.
% 2.42/1.77 % [INFO] Problem is first-order (TPTP FOF).
% 2.42/1.78 % [INFO] Type checking passed.
% 2.42/1.78 % [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 ...
% 4.98/2.71 % External prover 'e' found a proof!
% 4.98/2.71 % [INFO] Killing All external provers ...
% 4.98/2.71 % Time passed: 2145ms (effective reasoning time: 1488ms)
% 4.98/2.71 % Axioms used in derivation (18): axiom_7, axiom_10, axiom_15, axiom_2, axiom_6, axiom_16, axiom_3, axiom_1, axiom_8, axiom_17, axiom_0, axiom_11, axiom_12, axiom_9, axiom_14, axiom_4, axiom_5, axiom_13
% 4.98/2.71 % No. of inferences in proof: 37
% 4.98/2.71 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2145 ms resp. 1488 ms w/o parsing
% 4.98/2.78 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.98/2.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------