%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP545-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 : Thu Sep 24 08:41:57 AM UTC 2026
% Result : Unsatisfiable 268.25s 268.62s
% Output : Proof 268.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 45 ( 32 unt; 0 nHn; 41 RR)
% Number of literals : 67 ( 49 equ; 24 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiply,axiom,
multiply(A,B) = divide(A,divide(identity,B)),
file('theBenchmark.p',multiply) ).
cnf(inverse,axiom,
inverse(A) = divide(identity,A),
file('theBenchmark.p',inverse) ).
cnf(identity,axiom,
identity = divide(A,A),
file('theBenchmark.p',identity) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( divide(Eq_x_0,Eq_x_1) = divide(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(start,[status(thm),parent(0:0)],[prove_these_axioms_1]) ).
cnf(t2,plain,
( divide(inverse(a1),inverse(a1)) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) != divide(inverse(a1),inverse(a1))
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( divide(inverse(a1),divide(identity,a1)) != divide(inverse(a1),inverse(a1))
| multiply(inverse(a1),a1) != divide(inverse(a1),divide(identity,a1))
| multiply(inverse(a1),a1) = divide(inverse(a1),inverse(a1)) ),
inference(extension,[status(thm),parent(t2:2)],[equality_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
multiply(inverse(a1),a1) = divide(inverse(a1),divide(identity,a1)),
inference(extension,[status(thm),parent(t4:2)],[multiply]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( divide(identity,a1) != inverse(a1)
| inverse(a1) != inverse(a1)
| divide(inverse(a1),divide(identity,a1)) = divide(inverse(a1),inverse(a1)) ),
inference(extension,[status(thm),parent(t4:3)],[equality_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
inverse(a1) = inverse(a1),
inference(extension,[status(thm),parent(t8:2)],[equality_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( inverse(a1) != divide(identity,a1)
| divide(identity,a1) = inverse(a1) ),
inference(extension,[status(thm),parent(t8:3)],[equality_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
inverse(a1) = divide(identity,a1),
inference(extension,[status(thm),parent(t12:2)],[inverse]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( divide(inverse(b1),inverse(b1)) != multiply(inverse(b1),b1)
| divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1))
| divide(inverse(a1),inverse(a1)) = multiply(inverse(b1),b1) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:3]) ).
cnf(t18,plain,
( identity != divide(inverse(b1),inverse(b1))
| divide(inverse(a1),inverse(a1)) != identity
| divide(inverse(a1),inverse(a1)) = divide(inverse(b1),inverse(b1)) ),
inference(extension,[status(thm),parent(t16:2)],[equality_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( identity != divide(inverse(a1),inverse(a1))
| divide(inverse(a1),inverse(a1)) = identity ),
inference(extension,[status(thm),parent(t18:2)],[equality_2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
identity = divide(inverse(a1),inverse(a1)),
inference(extension,[status(thm),parent(t20:2)],[identity]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
identity = divide(inverse(b1),inverse(b1)),
inference(extension,[status(thm),parent(t18:3)],[identity]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t18:3]) ).
cnf(t26,plain,
( divide(inverse(b1),divide(identity,b1)) != multiply(inverse(b1),b1)
| divide(inverse(b1),inverse(b1)) != divide(inverse(b1),divide(identity,b1))
| divide(inverse(b1),inverse(b1)) = multiply(inverse(b1),b1) ),
inference(extension,[status(thm),parent(t16:3)],[equality_3]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t16:3]) ).
cnf(t28,plain,
( inverse(b1) != divide(identity,b1)
| inverse(b1) != inverse(b1)
| divide(inverse(b1),inverse(b1)) = divide(inverse(b1),divide(identity,b1)) ),
inference(extension,[status(thm),parent(t26:2)],[equality_4]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
inverse(b1) = inverse(b1),
inference(extension,[status(thm),parent(t28:2)],[equality_1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
inverse(b1) = divide(identity,b1),
inference(extension,[status(thm),parent(t28:3)],[inverse]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
( multiply(inverse(b1),b1) != divide(inverse(b1),divide(identity,b1))
| divide(inverse(b1),divide(identity,b1)) = multiply(inverse(b1),b1) ),
inference(extension,[status(thm),parent(t26:3)],[equality_2]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t26:3]) ).
cnf(t36,plain,
multiply(inverse(b1),b1) = divide(inverse(b1),divide(identity,b1)),
inference(extension,[status(thm),parent(t34:2)],[multiply]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP545-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.02 This is a CNF_UNS_RFO_PEQ_UEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 09:44:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 268.25/268.62 % SZS status Unsatisfiable for theBenchmark
% 268.25/268.62 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------