%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP704-12 : 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 : n002.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 30.53s 35.85s
% Output : Proof 30.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 87 ( 62 unt; 0 nHn; 77 RR)
% Number of literals : 130 ( 91 equ; 45 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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 : 33 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f01,axiom,
mult(A,ld(A,B)) = B,
file('theBenchmark.p',f01) ).
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(f13,axiom,
op_f = mult(A,mult(B,ld(mult(A,B),op_c))),
file('theBenchmark.p',f13) ).
cnf(goal,negated_conjecture,
mult(x4,mult(op_f,x5)) != mult(mult(x4,op_f),x5),
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(x4,mult(op_f,x5)) != mult(mult(x4,op_f),x5),
inference(start,[status(thm),parent(0:0)],[goal]) ).
cnf(t2,plain,
( mult(mult(unit,x4),mult(mult(U_324,mult(op_c,ld(mult(U_324,op_c),op_c))),x5)) != mult(mult(x4,op_f),x5)
| mult(x4,mult(op_f,x5)) != mult(mult(unit,x4),mult(mult(U_324,mult(op_c,ld(mult(U_324,op_c),op_c))),x5))
| mult(x4,mult(op_f,x5)) = mult(mult(x4,op_f),x5) ),
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_f,x5) != mult(mult(U_324,mult(op_c,ld(mult(U_324,op_c),op_c))),x5)
| x4 != mult(unit,x4)
| mult(x4,mult(op_f,x5)) = mult(mult(unit,x4),mult(mult(U_324,mult(op_c,ld(mult(U_324,op_c),op_c))),x5)) ),
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,x4) != x4
| x4 = mult(unit,x4) ),
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,x4) = x4,
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,
( x5 != x5
| op_f != mult(U_324,mult(op_c,ld(mult(U_324,op_c),op_c)))
| mult(op_f,x5) = mult(mult(U_324,mult(op_c,ld(mult(U_324,op_c),op_c))),x5) ),
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_f = mult(U_324,mult(op_c,ld(mult(U_324,op_c),op_c))),
inference(extension,[status(thm),parent(t10:2)],[f13]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( mult(unit,x5) != x5
| x5 != mult(unit,x5)
| x5 = x5 ),
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,x5) != x5
| x5 = mult(unit,x5) ),
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,x5) = x5,
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,x5) = x5,
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(x4,mult(mult(mult(U_324,op_c),ld(mult(U_324,op_c),op_c)),mult(unit,x5))) != mult(mult(x4,op_f),x5)
| mult(mult(unit,x4),mult(mult(U_324,mult(op_c,ld(mult(U_324,op_c),op_c))),x5)) != mult(x4,mult(mult(mult(U_324,op_c),ld(mult(U_324,op_c),op_c)),mult(unit,x5)))
| mult(mult(unit,x4),mult(mult(U_324,mult(op_c,ld(mult(U_324,op_c),op_c))),x5)) = mult(mult(x4,op_f),x5) ),
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(mult(U_324,mult(op_c,ld(mult(U_324,op_c),op_c))),x5) != mult(mult(mult(U_324,op_c),ld(mult(U_324,op_c),op_c)),mult(unit,x5))
| mult(unit,x4) != x4
| mult(mult(unit,x4),mult(mult(U_324,mult(op_c,ld(mult(U_324,op_c),op_c))),x5)) = mult(x4,mult(mult(mult(U_324,op_c),ld(mult(U_324,op_c),op_c)),mult(unit,x5))) ),
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,x4) = x4,
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,
( x5 != mult(unit,x5)
| mult(U_324,mult(op_c,ld(mult(U_324,op_c),op_c))) != mult(mult(U_324,op_c),ld(mult(U_324,op_c),op_c))
| mult(mult(U_324,mult(op_c,ld(mult(U_324,op_c),op_c))),x5) = mult(mult(mult(U_324,op_c),ld(mult(U_324,op_c),op_c)),mult(unit,x5)) ),
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,
mult(U_324,mult(op_c,ld(mult(U_324,op_c),op_c))) = mult(mult(U_324,op_c),ld(mult(U_324,op_c),op_c)),
inference(extension,[status(thm),parent(t28:2)],[f10]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( mult(unit,x5) != x5
| x5 = mult(unit,x5) ),
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,x5) = x5,
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(unit,x4),mult(op_c,x5)) != mult(mult(x4,op_f),x5)
| mult(x4,mult(mult(mult(U_324,op_c),ld(mult(U_324,op_c),op_c)),mult(unit,x5))) != mult(mult(unit,x4),mult(op_c,x5))
| mult(x4,mult(mult(mult(U_324,op_c),ld(mult(U_324,op_c),op_c)),mult(unit,x5))) = mult(mult(x4,op_f),x5) ),
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(mult(mult(U_324,op_c),ld(mult(U_324,op_c),op_c)),mult(unit,x5)) != mult(op_c,x5)
| x4 != mult(unit,x4)
| mult(x4,mult(mult(mult(U_324,op_c),ld(mult(U_324,op_c),op_c)),mult(unit,x5))) = mult(mult(unit,x4),mult(op_c,x5)) ),
inference(extension,[status(thm),parent(t36:2)],[equality_5]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
( mult(unit,x4) != x4
| x4 = mult(unit,x4) ),
inference(extension,[status(thm),parent(t38:2)],[equality_2]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
mult(unit,x4) = x4,
inference(extension,[status(thm),parent(t40:2)],[f06]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( mult(unit,x5) != x5
| mult(mult(U_324,op_c),ld(mult(U_324,op_c),op_c)) != op_c
| mult(mult(mult(U_324,op_c),ld(mult(U_324,op_c),op_c)),mult(unit,x5)) = mult(op_c,x5) ),
inference(extension,[status(thm),parent(t38:3)],[equality_5]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t38:3]) ).
cnf(t46,plain,
mult(mult(U_324,op_c),ld(mult(U_324,op_c),op_c)) = op_c,
inference(extension,[status(thm),parent(t44:2)],[f01]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
mult(unit,x5) = x5,
inference(extension,[status(thm),parent(t44:3)],[f06]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t44:3]) ).
cnf(t50,plain,
( mult(mult(mult(unit,x4),op_c),x5) != mult(mult(x4,op_f),x5)
| mult(mult(unit,x4),mult(op_c,x5)) != mult(mult(mult(unit,x4),op_c),x5)
| mult(mult(unit,x4),mult(op_c,x5)) = mult(mult(x4,op_f),x5) ),
inference(extension,[status(thm),parent(t36:3)],[equality_3]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t36:3]) ).
cnf(t52,plain,
mult(mult(unit,x4),mult(op_c,x5)) = mult(mult(mult(unit,x4),op_c),x5),
inference(extension,[status(thm),parent(t50:2)],[f10]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
( x5 != x5
| mult(mult(unit,x4),op_c) != mult(x4,op_f)
| mult(mult(mult(unit,x4),op_c),x5) = mult(mult(x4,op_f),x5) ),
inference(extension,[status(thm),parent(t50:3)],[equality_5]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t50:3]) ).
cnf(t56,plain,
( op_c != op_f
| mult(unit,x4) != x4
| mult(mult(unit,x4),op_c) = mult(x4,op_f) ),
inference(extension,[status(thm),parent(t54:2)],[equality_5]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
mult(unit,x4) = x4,
inference(extension,[status(thm),parent(t56:2)],[f06]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t56:2]) ).
cnf(t60,plain,
( op_f != op_c
| op_c = op_f ),
inference(extension,[status(thm),parent(t56:3)],[equality_2]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t56:3]) ).
cnf(t62,plain,
( mult(U_370,mult(op_c,ld(mult(U_370,op_c),op_c))) != op_c
| op_f != mult(U_370,mult(op_c,ld(mult(U_370,op_c),op_c)))
| op_f = op_c ),
inference(extension,[status(thm),parent(t60:2)],[equality_3]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t60:2]) ).
cnf(t64,plain,
op_f = mult(U_370,mult(op_c,ld(mult(U_370,op_c),op_c))),
inference(extension,[status(thm),parent(t62:2)],[f13]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t62:2]) ).
cnf(t66,plain,
( mult(mult(U_370,op_c),ld(mult(U_370,op_c),op_c)) != op_c
| mult(U_370,mult(op_c,ld(mult(U_370,op_c),op_c))) != mult(mult(U_370,op_c),ld(mult(U_370,op_c),op_c))
| mult(U_370,mult(op_c,ld(mult(U_370,op_c),op_c))) = op_c ),
inference(extension,[status(thm),parent(t62:3)],[equality_3]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t62:3]) ).
cnf(t68,plain,
mult(U_370,mult(op_c,ld(mult(U_370,op_c),op_c))) = mult(mult(U_370,op_c),ld(mult(U_370,op_c),op_c)),
inference(extension,[status(thm),parent(t66:2)],[f10]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t66:2]) ).
cnf(t70,plain,
mult(mult(U_370,op_c),ld(mult(U_370,op_c),op_c)) = op_c,
inference(extension,[status(thm),parent(t66:3)],[f01]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t66:3]) ).
cnf(t72,plain,
( mult(unit,x5) != x5
| x5 != mult(unit,x5)
| x5 = x5 ),
inference(extension,[status(thm),parent(t54:3)],[equality_3]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t54:3]) ).
cnf(t74,plain,
( mult(unit,x5) != x5
| x5 = mult(unit,x5) ),
inference(extension,[status(thm),parent(t72:2)],[equality_2]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t72:2]) ).
cnf(t76,plain,
mult(unit,x5) = x5,
inference(extension,[status(thm),parent(t74:2)],[f06]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t74:2]) ).
cnf(t78,plain,
mult(unit,x5) = x5,
inference(extension,[status(thm),parent(t72:3)],[f06]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t72:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP704-12 : 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
% 0.09/5.37 % Computer : n002.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 19 10:24:26 UTC 2026
% 0.09/5.38 % CPUTime :
% 30.53/35.85 % SZS status Unsatisfiable for theBenchmark
% 30.53/35.85 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------