%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP702-12 : TPTP v9.3.1. Released v8.1.0.
% 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 : n019.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 08:42:17 AM UTC 2026
% Result : Unsatisfiable 30.26s 30.58s
% Output : Proof 30.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 69 ( 49 unt; 0 nHn; 65 RR)
% Number of literals : 103 ( 73 equ; 36 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f02,axiom,
ld(A,mult(A,B)) = B,
file('theBenchmark.p',f02) ).
cnf(f06,axiom,
mult(unit,A) = A,
file('theBenchmark.p',f06) ).
cnf(f10,axiom,
mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
file('theBenchmark.p',f10) ).
cnf(f11,axiom,
op_d = ld(A,mult(op_c,A)),
file('theBenchmark.p',f11) ).
cnf(goal,negated_conjecture,
mult(x0,mult(op_d,x1)) != mult(mult(x0,op_d),x1),
file('theBenchmark.p',goal) ).
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_5,axiom,
( mult(Eq_x_0,Eq_x_1) = mult(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,
mult(x0,mult(op_d,x1)) != mult(mult(x0,op_d),x1),
inference(start,[status(thm),parent(0:0)],[goal]) ).
cnf(t2,plain,
( mult(mult(unit,x0),mult(ld(op_c,mult(op_c,op_c)),x1)) != mult(mult(x0,op_d),x1)
| mult(x0,mult(op_d,x1)) != mult(mult(unit,x0),mult(ld(op_c,mult(op_c,op_c)),x1))
| mult(x0,mult(op_d,x1)) = mult(mult(x0,op_d),x1) ),
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,
( mult(op_d,x1) != mult(ld(op_c,mult(op_c,op_c)),x1)
| x0 != mult(unit,x0)
| mult(x0,mult(op_d,x1)) = mult(mult(unit,x0),mult(ld(op_c,mult(op_c,op_c)),x1)) ),
inference(extension,[status(thm),parent(t2:2)],[equality_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( mult(unit,x0) != x0
| x0 = mult(unit,x0) ),
inference(extension,[status(thm),parent(t4:2)],[equality_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
mult(unit,x0) = x0,
inference(extension,[status(thm),parent(t6:2)],[f06]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( x1 != x1
| op_d != ld(op_c,mult(op_c,op_c))
| mult(op_d,x1) = mult(ld(op_c,mult(op_c,op_c)),x1) ),
inference(extension,[status(thm),parent(t4:3)],[equality_5]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:3]) ).
cnf(t12,plain,
op_d = ld(op_c,mult(op_c,op_c)),
inference(extension,[status(thm),parent(t10:2)],[f11]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( mult(unit,x1) != x1
| x1 != mult(unit,x1)
| x1 = x1 ),
inference(extension,[status(thm),parent(t10:3)],[equality_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
( mult(unit,x1) != x1
| x1 = mult(unit,x1) ),
inference(extension,[status(thm),parent(t14:2)],[equality_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
mult(unit,x1) = x1,
inference(extension,[status(thm),parent(t16:2)],[f06]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
mult(unit,x1) = x1,
inference(extension,[status(thm),parent(t14:3)],[f06]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:3]) ).
cnf(t22,plain,
( mult(x0,mult(op_c,mult(unit,x1))) != mult(mult(x0,op_d),x1)
| mult(mult(unit,x0),mult(ld(op_c,mult(op_c,op_c)),x1)) != mult(x0,mult(op_c,mult(unit,x1)))
| mult(mult(unit,x0),mult(ld(op_c,mult(op_c,op_c)),x1)) = mult(mult(x0,op_d),x1) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:3]) ).
cnf(t24,plain,
( mult(ld(op_c,mult(op_c,op_c)),x1) != mult(op_c,mult(unit,x1))
| mult(unit,x0) != x0
| mult(mult(unit,x0),mult(ld(op_c,mult(op_c,op_c)),x1)) = mult(x0,mult(op_c,mult(unit,x1))) ),
inference(extension,[status(thm),parent(t22:2)],[equality_5]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
mult(unit,x0) = x0,
inference(extension,[status(thm),parent(t24:2)],[f06]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( x1 != mult(unit,x1)
| ld(op_c,mult(op_c,op_c)) != op_c
| mult(ld(op_c,mult(op_c,op_c)),x1) = mult(op_c,mult(unit,x1)) ),
inference(extension,[status(thm),parent(t24:3)],[equality_5]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
cnf(t30,plain,
ld(op_c,mult(op_c,op_c)) = op_c,
inference(extension,[status(thm),parent(t28:2)],[f02]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( mult(unit,x1) != x1
| x1 = mult(unit,x1) ),
inference(extension,[status(thm),parent(t28:3)],[equality_2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
mult(unit,x1) = x1,
inference(extension,[status(thm),parent(t32:2)],[f06]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
( mult(mult(x0,op_c),mult(unit,x1)) != mult(mult(x0,op_d),x1)
| mult(x0,mult(op_c,mult(unit,x1))) != mult(mult(x0,op_c),mult(unit,x1))
| mult(x0,mult(op_c,mult(unit,x1))) = mult(mult(x0,op_d),x1) ),
inference(extension,[status(thm),parent(t22:3)],[equality_3]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t22:3]) ).
cnf(t38,plain,
mult(x0,mult(op_c,mult(unit,x1))) = mult(mult(x0,op_c),mult(unit,x1)),
inference(extension,[status(thm),parent(t36:2)],[f10]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
( mult(unit,x1) != x1
| mult(x0,op_c) != mult(x0,op_d)
| mult(mult(x0,op_c),mult(unit,x1)) = mult(mult(x0,op_d),x1) ),
inference(extension,[status(thm),parent(t36:3)],[equality_5]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t36:3]) ).
cnf(t42,plain,
( op_c != op_d
| x0 != x0
| mult(x0,op_c) = mult(x0,op_d) ),
inference(extension,[status(thm),parent(t40:2)],[equality_5]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( mult(unit,x0) != x0
| x0 != mult(unit,x0)
| x0 = x0 ),
inference(extension,[status(thm),parent(t42:2)],[equality_3]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
( mult(unit,x0) != x0
| x0 = mult(unit,x0) ),
inference(extension,[status(thm),parent(t44:2)],[equality_2]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
mult(unit,x0) = x0,
inference(extension,[status(thm),parent(t46:2)],[f06]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
mult(unit,x0) = x0,
inference(extension,[status(thm),parent(t44:3)],[f06]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t44:3]) ).
cnf(t52,plain,
( op_d != op_c
| op_c = op_d ),
inference(extension,[status(thm),parent(t42:3)],[equality_2]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t42:3]) ).
cnf(t54,plain,
( ld(op_c,mult(op_c,op_c)) != op_c
| op_d != ld(op_c,mult(op_c,op_c))
| op_d = op_c ),
inference(extension,[status(thm),parent(t52:2)],[equality_3]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
op_d = ld(op_c,mult(op_c,op_c)),
inference(extension,[status(thm),parent(t54:2)],[f11]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
ld(op_c,mult(op_c,op_c)) = op_c,
inference(extension,[status(thm),parent(t54:3)],[f02]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t54:3]) ).
cnf(t60,plain,
mult(unit,x1) = x1,
inference(extension,[status(thm),parent(t40:3)],[f06]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t40:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP702-12 : TPTP v9.3.1. Released v8.1.0.
% 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
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 19 10:21:05 UTC 2026
% 0.11/0.37 % CPUTime :
% 30.26/30.58 % SZS status Unsatisfiable for theBenchmark
% 30.26/30.58 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------