%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP236-1 : TPTP v9.3.1. Released v2.5.0.
% 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 : n012.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 07:20:32 AM UTC 2026
% Result : Unsatisfiable 3.91s 2.17s
% Output : Refutation 4.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 30
% Syntax : Number of formulae : 61 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 131 ( 130 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 314 ( 22 ~; 70 |; 0 &; 222 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(inverse_decl,type,
inverse: $i > $i ).
thf(sk_c8_decl,type,
sk_c8: $i ).
thf(sk_c7_decl,type,
sk_c7: $i ).
thf(sk_c1_decl,type,
sk_c1: $i ).
thf(sk_c4_decl,type,
sk_c4: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(sk_c6_decl,type,
sk_c6: $i ).
thf(sk_c5_decl,type,
sk_c5: $i ).
thf(sk_c2_decl,type,
sk_c2: $i ).
thf(sk_c3_decl,type,
sk_c3: $i ).
thf(identity_decl,type,
identity: $i ).
thf(26,negated_conjecture,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
thf(56,plain,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(24,negated_conjecture,
( ( ( sk_c6 @ ( sk_c8 @ multiply ) )
= sk_c7 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
thf(52,plain,
( ( ( sk_c6 @ ( sk_c8 @ multiply ) )
= sk_c7 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
thf(116,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(25,negated_conjecture,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c6 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
thf(53,plain,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c6 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(17,negated_conjecture,
( ( ( sk_c4 @ inverse )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
thf(41,plain,
( ( ( sk_c4 @ inverse )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,negated_conjecture,
( ( ( sk_c7 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
thf(44,plain,
( ( ( sk_c7 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,negated_conjecture,
( ( ( sk_c7 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
thf(39,plain,
( ( ( sk_c7 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,negated_conjecture,
( ( sk_c8 @ inverse )
= sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
thf(35,plain,
( ( sk_c8 @ inverse )
= sk_c7 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(112,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(8,negated_conjecture,
( ( ( sk_c7 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c7 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
thf(48,plain,
( ( ( sk_c7 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c7 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,negated_conjecture,
( ( ( sk_c4 @ inverse )
= sk_c8 )
| ( ( sk_c7 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
thf(43,plain,
( ( ( sk_c4 @ inverse )
= sk_c8 )
| ( ( sk_c7 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,negated_conjecture,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c7 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
thf(47,plain,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c7 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,negated_conjecture,
( ( ( sk_c4 @ inverse )
= sk_c8 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
thf(42,plain,
( ( ( sk_c4 @ inverse )
= sk_c8 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(21,negated_conjecture,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
thf(37,plain,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(16,negated_conjecture,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
thf(46,plain,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(23,negated_conjecture,
( ( ( sk_c7 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
thf(57,plain,
( ( ( sk_c7 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(9,negated_conjecture,
( ( ( sk_c6 @ ( sk_c8 @ multiply ) )
= sk_c7 )
| ( ( sk_c7 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
thf(38,plain,
( ( ( sk_c6 @ ( sk_c8 @ multiply ) )
= sk_c7 )
| ( ( sk_c7 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,negated_conjecture,
( ( ( sk_c6 @ ( sk_c8 @ multiply ) )
= sk_c7 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
thf(33,plain,
( ( ( sk_c6 @ ( sk_c8 @ multiply ) )
= sk_c7 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,negated_conjecture,
( ( ( sk_c7 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
thf(45,plain,
( ( ( sk_c7 @ ( sk_c4 @ multiply ) )
= sk_c8 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,negated_conjecture,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c6 )
| ( ( sk_c7 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
thf(32,plain,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c6 )
| ( ( sk_c7 @ ( sk_c1 @ multiply ) )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20,negated_conjecture,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c6 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
thf(34,plain,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c6 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(22,negated_conjecture,
( ( ( sk_c4 @ inverse )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
thf(54,plain,
( ( ( sk_c4 @ inverse )
= sk_c8 )
| ( ( sk_c8 @ ( sk_c3 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(19,negated_conjecture,
( ( ( sk_c6 @ ( sk_c8 @ multiply ) )
= sk_c7 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
thf(49,plain,
( ( ( sk_c6 @ ( sk_c8 @ multiply ) )
= sk_c7 )
| ( ( sk_c2 @ inverse )
= sk_c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,negated_conjecture,
( ( ( sk_c6 @ ( sk_c8 @ multiply ) )
= sk_c7 )
| ( ( sk_c1 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
thf(50,plain,
( ( ( sk_c6 @ ( sk_c8 @ multiply ) )
= sk_c7 )
| ( ( sk_c1 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,negated_conjecture,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c6 )
| ( ( sk_c1 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
thf(31,plain,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c6 )
| ( ( sk_c1 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,negated_conjecture,
( ( ( sk_c4 @ inverse )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
thf(40,plain,
( ( ( sk_c4 @ inverse )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(27,negated_conjecture,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ inverse )
!= sk_c8 )
| ( ( sk_c8 @ ( F @ multiply ) )
!= E )
| ( ( E @ ( sk_c8 @ multiply ) )
!= sk_c7 )
| ( ( sk_c7 @ ( D @ multiply ) )
!= sk_c8 )
| ( ( D @ inverse )
!= sk_c8 )
| ( ( sk_c8 @ ( C @ multiply ) )
!= sk_c7 )
| ( ( B @ inverse )
!= C )
| ( ( C @ ( B @ multiply ) )
!= sk_c7 )
| ( ( sk_c7 @ ( A @ multiply ) )
!= sk_c8 )
| ( ( A @ inverse )
!= sk_c8 )
| ( ( sk_c8 @ inverse )
!= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
thf(55,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ inverse )
!= sk_c8 )
| ( ( sk_c8 @ ( F @ multiply ) )
!= E )
| ( ( E @ ( sk_c8 @ multiply ) )
!= sk_c7 )
| ( ( sk_c7 @ ( D @ multiply ) )
!= sk_c8 )
| ( ( D @ inverse )
!= sk_c8 )
| ( ( sk_c8 @ ( C @ multiply ) )
!= sk_c7 )
| ( ( B @ inverse )
!= C )
| ( ( C @ ( B @ multiply ) )
!= sk_c7 )
| ( ( sk_c7 @ ( A @ multiply ) )
!= sk_c8 )
| ( ( A @ inverse )
!= sk_c8 )
| ( ( sk_c8 @ inverse )
!= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(114,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(6,negated_conjecture,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
thf(36,plain,
( ( ( sk_c5 @ inverse )
= sk_c8 )
| ( ( sk_c1 @ inverse )
= sk_c8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,negated_conjecture,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c6 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
thf(51,plain,
( ( ( sk_c8 @ ( sk_c5 @ multiply ) )
= sk_c6 )
| ( ( sk_c3 @ ( sk_c2 @ multiply ) )
= sk_c7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(126,plain,
$false,
inference(e,[status(thm)],[56,52,116,53,41,44,39,35,112,48,43,47,42,37,46,57,38,33,45,32,34,54,49,50,31,40,55,114,36,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP236-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % 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
% 0.05/0.32 % Computer : n012.cluster.edu
% 0.05/0.32 % Model : x86_64 x86_64
% 0.05/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.32 % Memory : 8046.5625MB
% 0.05/0.32 % OS : Linux 6.8.0-71-generic
% 0.05/0.32 % CPULimit : 300
% 0.05/0.32 % WCLimit : 300
% 0.05/0.32 % DateTime : Fri Sep 25 14:39:50 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 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
% 0.60/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.95/0.95 % [INFO] Parsing done (172ms).
% 0.95/0.96 % [INFO] Running in sequential loop mode.
% 1.56/1.29 % [INFO] eprover registered as external prover.
% 1.76/1.30 % [INFO] Scanning for conjecture ...
% 1.96/1.42 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.96/1.48 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.96/1.48 % [INFO] Problem is propositional (TPTP CNF).
% 1.96/1.48 % [INFO] Type checking passed.
% 1.96/1.49 % [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 ...
% 3.91/2.17 % External prover 'e' found a proof!
% 3.91/2.17 % [INFO] Killing All external provers ...
% 3.91/2.17 % Time passed: 1758ms (effective reasoning time: 1208ms)
% 3.91/2.17 % Axioms used in derivation (3): associativity, left_identity, left_inverse
% 3.91/2.17 % No. of inferences in proof: 61
% 3.91/2.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1758 ms resp. 1208 ms w/o parsing
% 4.08/2.22 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.08/2.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------