%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS073+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 : n005.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 07:44:35 AM UTC 2026
% Result : Unsatisfiable 4.97s 2.24s
% Output : Refutation 5.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 30
% Syntax : Number of formulae : 61 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 189 ( 42 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 380 ( 8 ~; 0 |; 61 &; 244 @)
% ( 5 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 152 ( 0 ^; 146 !; 6 ?; 152 :)
% Comments :
%------------------------------------------------------------------------------
thf(cUnsatisfiable_decl,type,
cUnsatisfiable: $i > $o ).
thf(cowlNothing_decl,type,
cowlNothing: $i > $o ).
thf(cowlThing_decl,type,
cowlThing: $i > $o ).
thf(cp_decl,type,
cp: $i > $o ).
thf(rf_decl,type,
rf: $i > $i > $o ).
thf(rf1_decl,type,
rf1: $i > $i > $o ).
thf(rinvF_decl,type,
rinvF: $i > $i > $o ).
thf(rinvF1_decl,type,
rinvF1: $i > $i > $o ).
thf(rinvS_decl,type,
rinvS: $i > $i > $o ).
thf(rs_decl,type,
rs: $i > $i > $o ).
thf(xsd_integer_decl,type,
xsd_integer: $i > $o ).
thf(xsd_string_decl,type,
xsd_string: $i > $o ).
thf(i2003_11_14_17_18_54369_decl,type,
i2003_11_14_17_18_54369: $i ).
thf(21,axiom,
! [A: $i] :
( ( A @ cUnsatisfiable )
<=> ( ~ ( A @ cp )
& ? [B: $i] :
( ! [C: $i] :
( ( C @ ( B @ rinvF ) )
=> ? [D: $i] :
( ( D @ cp )
& ( D @ ( C @ rs ) ) ) )
& ! [C: $i] :
( ( C @ ( B @ rinvS ) )
=> ( C @ cp ) )
& ( B @ ( A @ rf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(115,plain,
! [A: $i] :
( ( ( ~ ( A @ cp )
& ? [B: $i] :
( ! [C: $i] :
( ( C @ ( B @ rinvF ) )
=> ? [D: $i] :
( ( D @ cp )
& ( D @ ( C @ rs ) ) ) )
& ! [C: $i] :
( ( C @ ( B @ rinvS ) )
=> ( C @ cp ) )
& ( B @ ( A @ rf ) ) ) )
=> ( A @ cUnsatisfiable ) )
& ( ( A @ cUnsatisfiable )
=> ( ~ ( A @ cp )
& ? [B: $i] :
( ! [C: $i] :
( ( C @ ( B @ rinvF ) )
=> ? [D: $i] :
( ( D @ cp )
& ( D @ ( C @ rs ) ) ) )
& ! [C: $i] :
( ( C @ ( B @ rinvS ) )
=> ( C @ cp ) )
& ( B @ ( A @ rf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rs ) )
& ( B @ ( A @ rs ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
thf(157,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rs ) )
& ( B @ ( A @ rs ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf ) )
& ( B @ ( A @ rf ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(133,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf ) )
& ( B @ ( A @ rf ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(28,axiom,
i2003_11_14_17_18_54369 @ cUnsatisfiable,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
thf(160,plain,
i2003_11_14_17_18_54369 @ cUnsatisfiable,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(109,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rs ) )
=> ( B @ ( A @ rf1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(161,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rs ) )
=> ( B @ ( A @ rf1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rf1 ) )
& ( A = B ) )
=> ( B @ ( C @ rf1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf1_substitution_2) ).
thf(59,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rf1 ) )
& ( A = B ) )
=> ( B @ ( C @ rf1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvF1 ) )
& ( A = B ) )
=> ( C @ ( B @ rinvF1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvF1_substitution_1) ).
thf(71,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvF1 ) )
& ( A = B ) )
=> ( C @ ( B @ rinvF1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(39,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rinvF1 ) )
<=> ( A @ ( B @ rf1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(145,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ rf1 ) )
=> ( B @ ( A @ rinvF1 ) ) )
& ( ( B @ ( A @ rinvF1 ) )
=> ( A @ ( B @ rf1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A @ cp )
& ( A = B ) )
=> ( B @ cp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp_substitution_1) ).
thf(43,plain,
! [A: $i,B: $i] :
( ( ( A @ cp )
& ( A = B ) )
=> ( B @ cp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rinvF1 ) )
& ( A = B ) )
=> ( B @ ( C @ rinvF1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvF1_substitution_2) ).
thf(75,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rinvF1 ) )
& ( A = B ) )
=> ( B @ ( C @ rinvF1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rinvS ) )
& ( A = B ) )
=> ( B @ ( C @ rinvS ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvS_substitution_2) ).
thf(83,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rinvS ) )
& ( A = B ) )
=> ( B @ ( C @ rinvS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(19,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
thf(103,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rs ) )
& ( A = B ) )
=> ( B @ ( C @ rs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rs_substitution_2) ).
thf(91,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rs ) )
& ( A = B ) )
=> ( B @ ( C @ rs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvF ) )
& ( A = B ) )
=> ( C @ ( B @ rinvF ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvF_substitution_1) ).
thf(63,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvF ) )
& ( A = B ) )
=> ( C @ ( B @ rinvF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xsd_integer_substitution_1) ).
thf(95,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rinvF ) )
& ( A = B ) )
=> ( B @ ( C @ rinvF ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvF_substitution_2) ).
thf(67,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rinvF ) )
& ( A = B ) )
=> ( B @ ( C @ rinvF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( ( A @ cUnsatisfiable )
& ( A = B ) )
=> ( B @ cUnsatisfiable ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cUnsatisfiable_substitution_1) ).
thf(31,plain,
! [A: $i,B: $i] :
( ( ( A @ cUnsatisfiable )
& ( A = B ) )
=> ( B @ cUnsatisfiable ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xsd_string_substitution_1) ).
thf(99,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rs ) )
& ( A = B ) )
=> ( C @ ( B @ rs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rs_substitution_1) ).
thf(87,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rs ) )
& ( A = B ) )
=> ( C @ ( B @ rs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf1 ) )
& ( A = B ) )
=> ( C @ ( B @ rf1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf1_substitution_1) ).
thf(55,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf1 ) )
& ( A = B ) )
=> ( C @ ( B @ rf1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rinvF ) )
<=> ( A @ ( B @ rf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ rf ) )
=> ( B @ ( A @ rinvF ) ) )
& ( ( B @ ( A @ rinvF ) )
=> ( A @ ( B @ rf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rinvS ) )
<=> ( A @ ( B @ rs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(151,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)],[26]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rf ) )
& ( A = B ) )
=> ( B @ ( C @ rf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf_substitution_2) ).
thf(51,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rf ) )
& ( A = B ) )
=> ( B @ ( C @ rf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf1 ) )
& ( B @ ( A @ rf1 ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(136,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf1 ) )
& ( B @ ( A @ rf1 ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvS ) )
& ( A = B ) )
=> ( C @ ( B @ rinvS ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvS_substitution_1) ).
thf(79,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvS ) )
& ( A = B ) )
=> ( C @ ( B @ rinvS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf ) )
& ( A = B ) )
=> ( C @ ( B @ rf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf_substitution_1) ).
thf(47,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf ) )
& ( A = B ) )
=> ( C @ ( B @ rf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rs ) )
=> ( B @ ( A @ rf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(163,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rs ) )
=> ( B @ ( A @ rf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(168,plain,
$false,
inference(e,[status(thm)],[115,157,133,160,109,161,59,71,39,35,145,43,75,83,103,91,63,95,67,31,99,87,55,139,151,51,136,79,47,163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS073+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
% 0.13/0.38 % Computer : n005.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Fri Sep 25 19:38:02 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 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
% 0.90/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.97 % [INFO] Parsing done (167ms).
% 1.16/0.98 % [INFO] Running in sequential loop mode.
% 2.11/1.30 % [INFO] eprover registered as external prover.
% 2.11/1.31 % [INFO] Scanning for conjecture ...
% 2.11/1.35 % [INFO] 30 axioms and no conjecture found.
% 2.33/1.43 % [INFO] Problem is first-order (TPTP FOF).
% 2.33/1.44 % [INFO] Type checking passed.
% 2.33/1.45 % [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 ...
% 4.97/2.23 % External prover 'e' found a proof!
% 4.97/2.23 % [INFO] Killing All external provers ...
% 4.97/2.23 % Time passed: 1725ms (effective reasoning time: 1248ms)
% 4.97/2.24 % Axioms used in derivation (30): rinvF1_substitution_1, axiom_2, axiom_6, rinvS_substitution_2, cowlThing_substitution_1, axiom_3, cUnsatisfiable_substitution_1, rinvS_substitution_1, axiom_5, axiom_11, rf_substitution_1, cp_substitution_1, axiom_4, axiom_7, cowlNothing_substitution_1, rinvF_substitution_2, axiom_10, xsd_string_substitution_1, rf1_substitution_2, axiom_1, xsd_integer_substitution_1, rf1_substitution_1, axiom_8, rs_substitution_2, rinvF1_substitution_2, rinvF_substitution_1, rf_substitution_2, axiom_0, axiom_9, rs_substitution_1
% 4.97/2.24 % No. of inferences in proof: 61
% 4.97/2.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1725 ms resp. 1248 ms w/o parsing
% 5.29/2.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.29/2.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------