%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP537-1 : 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 : n001.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 08:41:56 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.77s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of clauses : 38 ( 27 unt; 0 nHn; 32 RR)
% Number of literals : 58 ( 44 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(A,B),divide(divide(A,C),B)) = C,
file('theBenchmark.p',single_axiom) ).
cnf(multiply,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('theBenchmark.p',multiply) ).
cnf(inverse,axiom,
inverse(A) = divide(divide(B,B),A),
file('theBenchmark.p',inverse) ).
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(equality_5,axiom,
( multiply(Eq_x_0,Eq_x_1) = multiply(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(b1),inverse(b1)) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) != divide(inverse(b1),inverse(b1))
| 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,
( multiply(divide(divide(inverse(b1),inverse(b1)),a1),a1) != divide(inverse(b1),inverse(b1))
| multiply(inverse(a1),a1) != multiply(divide(divide(inverse(b1),inverse(b1)),a1),a1)
| multiply(inverse(a1),a1) = divide(inverse(b1),inverse(b1)) ),
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,
( a1 != a1
| inverse(a1) != divide(divide(inverse(b1),inverse(b1)),a1)
| multiply(inverse(a1),a1) = multiply(divide(divide(inverse(b1),inverse(b1)),a1),a1) ),
inference(extension,[status(thm),parent(t4:2)],[equality_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
inverse(a1) = divide(divide(inverse(b1),inverse(b1)),a1),
inference(extension,[status(thm),parent(t6:2)],[inverse]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
a1 = a1,
inference(extension,[status(thm),parent(t6:3)],[equality_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( divide(divide(divide(inverse(b1),inverse(b1)),a1),divide(divide(divide(inverse(b1),inverse(b1)),divide(inverse(b1),inverse(b1))),a1)) != divide(inverse(b1),inverse(b1))
| multiply(divide(divide(inverse(b1),inverse(b1)),a1),a1) != divide(divide(divide(inverse(b1),inverse(b1)),a1),divide(divide(divide(inverse(b1),inverse(b1)),divide(inverse(b1),inverse(b1))),a1))
| multiply(divide(divide(inverse(b1),inverse(b1)),a1),a1) = divide(inverse(b1),inverse(b1)) ),
inference(extension,[status(thm),parent(t4:3)],[equality_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
multiply(divide(divide(inverse(b1),inverse(b1)),a1),a1) = divide(divide(divide(inverse(b1),inverse(b1)),a1),divide(divide(divide(inverse(b1),inverse(b1)),divide(inverse(b1),inverse(b1))),a1)),
inference(extension,[status(thm),parent(t12:2)],[multiply]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
divide(divide(divide(inverse(b1),inverse(b1)),a1),divide(divide(divide(inverse(b1),inverse(b1)),divide(inverse(b1),inverse(b1))),a1)) = divide(inverse(b1),inverse(b1)),
inference(extension,[status(thm),parent(t12:3)],[single_axiom]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
( divide(inverse(b1),divide(divide(U_178,U_178),b1)) != multiply(inverse(b1),b1)
| divide(inverse(b1),inverse(b1)) != divide(inverse(b1),divide(divide(U_178,U_178),b1))
| divide(inverse(b1),inverse(b1)) = multiply(inverse(b1),b1) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t2:3]) ).
cnf(t20,plain,
( inverse(b1) != divide(divide(U_178,U_178),b1)
| inverse(b1) != inverse(b1)
| divide(inverse(b1),inverse(b1)) = divide(inverse(b1),divide(divide(U_178,U_178),b1)) ),
inference(extension,[status(thm),parent(t18:2)],[equality_4]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
inverse(b1) = inverse(b1),
inference(extension,[status(thm),parent(t20:2)],[equality_1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
inverse(b1) = divide(divide(U_178,U_178),b1),
inference(extension,[status(thm),parent(t20:3)],[inverse]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
( multiply(inverse(b1),b1) != divide(inverse(b1),divide(divide(U_178,U_178),b1))
| divide(inverse(b1),divide(divide(U_178,U_178),b1)) = multiply(inverse(b1),b1) ),
inference(extension,[status(thm),parent(t18:3)],[equality_2]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t18:3]) ).
cnf(t28,plain,
multiply(inverse(b1),b1) = divide(inverse(b1),divide(divide(U_178,U_178),b1)),
inference(extension,[status(thm),parent(t26:2)],[multiply]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP537-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 This is a CNF_UNS_RFO_PEQ_UEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n001.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Sat Sep 19 09:46:40 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.14/0.77 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.77 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------