%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP684-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 08:42:15 AM UTC 2026
% Result : Unsatisfiable 277.44s 277.77s
% Output : Proof 277.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 91 ( 64 unt; 0 nHn; 84 RR)
% Number of literals : 136 ( 97 equ; 47 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c01,axiom,
ld(A,mult(A,A)) = A,
file('theBenchmark.p',c01) ).
cnf(c02,axiom,
rd(mult(A,A),A) = A,
file('theBenchmark.p',c02) ).
cnf(c03,axiom,
mult(A,ld(A,B)) = ld(A,mult(A,B)),
file('theBenchmark.p',c03) ).
cnf(c06,axiom,
rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
file('theBenchmark.p',c06) ).
cnf(goals,negated_conjecture,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
file('theBenchmark.p',goals) ).
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,
( 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(equality_6,axiom,
( rd(Eq_x_0,Eq_x_1) = rd(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,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
inference(start,[status(thm),parent(0:0)],[goals]) ).
cnf(t2,plain,
( rd(mult(a,c),c) != rd(mult(a,mult(b,c)),mult(b,c))
| rd(mult(a,mult(b,c)),mult(b,c)) = rd(mult(a,c),c) ),
inference(extension,[status(thm),parent(t1:1)],[equality_2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( rd(mult(mult(a,ld(a,a)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)) != rd(mult(a,mult(b,c)),mult(b,c))
| rd(mult(a,c),c) != rd(mult(mult(a,ld(a,a)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)),rd(mult(mult(b,c),rd(mult(c,c),c)),c))
| rd(mult(a,c),c) = rd(mult(a,mult(b,c)),mult(b,c)) ),
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,
( rd(mult(mult(a,ld(a,a)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)) != rd(mult(a,c),c)
| rd(mult(a,c),c) = rd(mult(mult(a,ld(a,a)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)) ),
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(a,rd(mult(ld(a,a),c),c)) != rd(mult(a,c),c)
| rd(mult(mult(a,ld(a,a)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)) != mult(a,rd(mult(ld(a,a),c),c))
| rd(mult(mult(a,ld(a,a)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)) = rd(mult(a,c),c) ),
inference(extension,[status(thm),parent(t6:2)],[equality_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
rd(mult(mult(a,ld(a,a)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)) = mult(a,rd(mult(ld(a,a),c),c)),
inference(extension,[status(thm),parent(t8:2)],[c06]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( rd(mult(mult(a,ld(a,a)),rd(mult(c,c),c)),rd(mult(c,c),c)) != rd(mult(a,c),c)
| mult(a,rd(mult(ld(a,a),c),c)) != rd(mult(mult(a,ld(a,a)),rd(mult(c,c),c)),rd(mult(c,c),c))
| mult(a,rd(mult(ld(a,a),c),c)) = rd(mult(a,c),c) ),
inference(extension,[status(thm),parent(t8:3)],[equality_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( rd(mult(mult(a,ld(a,a)),rd(mult(c,c),c)),rd(mult(c,c),c)) != mult(a,rd(mult(ld(a,a),c),c))
| mult(a,rd(mult(ld(a,a),c),c)) = rd(mult(mult(a,ld(a,a)),rd(mult(c,c),c)),rd(mult(c,c),c)) ),
inference(extension,[status(thm),parent(t12:2)],[equality_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
rd(mult(mult(a,ld(a,a)),rd(mult(c,c),c)),rd(mult(c,c),c)) = mult(a,rd(mult(ld(a,a),c),c)),
inference(extension,[status(thm),parent(t14:2)],[c06]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( mult(mult(a,ld(a,a)),rd(mult(c,c),c)) != mult(a,c)
| rd(mult(c,c),c) != c
| rd(mult(mult(a,ld(a,a)),rd(mult(c,c),c)),rd(mult(c,c),c)) = rd(mult(a,c),c) ),
inference(extension,[status(thm),parent(t12:3)],[equality_6]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t12:3]) ).
cnf(t20,plain,
rd(mult(c,c),c) = c,
inference(extension,[status(thm),parent(t18:2)],[c02]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(l10,lemma,
rd(mult(c,c),c) = c,
inference(lemma,[status(cth),parent(t18:2),below(t12:3)],[t18:2]) ).
cnf(t22,plain,
( mult(a,ld(a,a)) != a
| rd(mult(c,c),c) != c
| mult(mult(a,ld(a,a)),rd(mult(c,c),c)) = mult(a,c) ),
inference(extension,[status(thm),parent(t18:3)],[equality_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
rd(mult(c,c),c) = c,
inference(lemma_extension,[status(thm),parent(t22:2)],[l10:1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( ld(a,mult(a,a)) != a
| mult(a,ld(a,a)) != ld(a,mult(a,a))
| mult(a,ld(a,a)) = a ),
inference(extension,[status(thm),parent(t22:3)],[equality_3]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
cnf(t28,plain,
mult(a,ld(a,a)) = ld(a,mult(a,a)),
inference(extension,[status(thm),parent(t26:2)],[c03]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
ld(a,mult(a,a)) = a,
inference(extension,[status(thm),parent(t26:3)],[c01]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t26:3]) ).
cnf(t32,plain,
( rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(mult(a,ld(a,a)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)),rd(mult(mult(b,c),rd(mult(c,c),c)),c))
| rd(mult(mult(a,ld(a,a)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)) = rd(mult(a,mult(b,c)),mult(b,c)) ),
inference(extension,[status(thm),parent(t4:3)],[equality_2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t4:3]) ).
cnf(t34,plain,
( mult(a,mult(b,c)) != mult(mult(a,ld(a,a)),rd(mult(mult(b,c),rd(mult(c,c),c)),c))
| mult(b,c) != rd(mult(mult(b,c),rd(mult(c,c),c)),c)
| rd(mult(a,mult(b,c)),mult(b,c)) = rd(mult(mult(a,ld(a,a)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)) ),
inference(extension,[status(thm),parent(t32:2)],[equality_6]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
( rd(mult(mult(b,c),rd(U_3553,c)),rd(U_3553,c)) != rd(mult(mult(b,c),rd(mult(c,c),c)),c)
| mult(b,c) != rd(mult(mult(b,c),rd(U_3553,c)),rd(U_3553,c))
| mult(b,c) = rd(mult(mult(b,c),rd(mult(c,c),c)),c) ),
inference(extension,[status(thm),parent(t34:2)],[equality_3]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
( rd(mult(mult(b,c),rd(U_3553,c)),rd(U_3553,c)) != mult(b,c)
| mult(b,c) = rd(mult(mult(b,c),rd(U_3553,c)),rd(U_3553,c)) ),
inference(extension,[status(thm),parent(t36:2)],[equality_2]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
( mult(b,rd(mult(c,c),c)) != mult(b,c)
| rd(mult(mult(b,c),rd(U_3553,c)),rd(U_3553,c)) != mult(b,rd(mult(c,c),c))
| rd(mult(mult(b,c),rd(U_3553,c)),rd(U_3553,c)) = mult(b,c) ),
inference(extension,[status(thm),parent(t38:2)],[equality_3]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
rd(mult(mult(b,c),rd(U_3553,c)),rd(U_3553,c)) = mult(b,rd(mult(c,c),c)),
inference(extension,[status(thm),parent(t40:2)],[c06]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( b != b
| rd(mult(c,c),c) != c
| mult(b,rd(mult(c,c),c)) = mult(b,c) ),
inference(extension,[status(thm),parent(t40:3)],[equality_4]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t40:3]) ).
cnf(t46,plain,
rd(mult(c,c),c) = c,
inference(extension,[status(thm),parent(t44:2)],[c02]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
b = b,
inference(extension,[status(thm),parent(t44:3)],[equality_1]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t44:3]) ).
cnf(t50,plain,
( mult(b,rd(mult(c,c),c)) != rd(mult(mult(b,c),rd(mult(c,c),c)),c)
| rd(mult(mult(b,c),rd(U_3553,c)),rd(U_3553,c)) != mult(b,rd(mult(c,c),c))
| rd(mult(mult(b,c),rd(U_3553,c)),rd(U_3553,c)) = rd(mult(mult(b,c),rd(mult(c,c),c)),c) ),
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,
rd(mult(mult(b,c),rd(U_3553,c)),rd(U_3553,c)) = mult(b,rd(mult(c,c),c)),
inference(extension,[status(thm),parent(t50:2)],[c06]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
( rd(mult(mult(b,c),rd(mult(c,c),c)),rd(mult(c,c),c)) != rd(mult(mult(b,c),rd(mult(c,c),c)),c)
| mult(b,rd(mult(c,c),c)) != rd(mult(mult(b,c),rd(mult(c,c),c)),rd(mult(c,c),c))
| mult(b,rd(mult(c,c),c)) = rd(mult(mult(b,c),rd(mult(c,c),c)),c) ),
inference(extension,[status(thm),parent(t50:3)],[equality_3]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t50:3]) ).
cnf(t56,plain,
( rd(mult(mult(b,c),rd(mult(c,c),c)),rd(mult(c,c),c)) != mult(b,rd(mult(c,c),c))
| mult(b,rd(mult(c,c),c)) = rd(mult(mult(b,c),rd(mult(c,c),c)),rd(mult(c,c),c)) ),
inference(extension,[status(thm),parent(t54:2)],[equality_2]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
rd(mult(mult(b,c),rd(mult(c,c),c)),rd(mult(c,c),c)) = mult(b,rd(mult(c,c),c)),
inference(extension,[status(thm),parent(t56:2)],[c06]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t56:2]) ).
cnf(t60,plain,
( mult(mult(b,c),rd(mult(c,c),c)) != mult(mult(b,c),rd(mult(c,c),c))
| rd(mult(c,c),c) != c
| rd(mult(mult(b,c),rd(mult(c,c),c)),rd(mult(c,c),c)) = rd(mult(mult(b,c),rd(mult(c,c),c)),c) ),
inference(extension,[status(thm),parent(t54:3)],[equality_6]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t54:3]) ).
cnf(t62,plain,
rd(mult(c,c),c) = c,
inference(extension,[status(thm),parent(t60:2)],[c02]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t60:2]) ).
cnf(t64,plain,
mult(mult(b,c),rd(mult(c,c),c)) = mult(mult(b,c),rd(mult(c,c),c)),
inference(extension,[status(thm),parent(t60:3)],[equality_1]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t60:3]) ).
cnf(l17,lemma,
mult(b,c) = rd(mult(mult(b,c),rd(mult(c,c),c)),c),
inference(lemma,[status(cth),parent(t34:2),below(t32:2)],[t34:2]) ).
cnf(t66,plain,
( mult(mult(a,ld(a,a)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)) != mult(a,mult(b,c))
| mult(a,mult(b,c)) = mult(mult(a,ld(a,a)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)) ),
inference(extension,[status(thm),parent(t34:3)],[equality_2]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t34:3]) ).
cnf(t68,plain,
( mult(a,ld(a,a)) != a
| rd(mult(mult(b,c),rd(mult(c,c),c)),c) != mult(b,c)
| mult(mult(a,ld(a,a)),rd(mult(mult(b,c),rd(mult(c,c),c)),c)) = mult(a,mult(b,c)) ),
inference(extension,[status(thm),parent(t66:2)],[equality_4]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t66:2]) ).
cnf(t70,plain,
( mult(b,c) != rd(mult(mult(b,c),rd(mult(c,c),c)),c)
| rd(mult(mult(b,c),rd(mult(c,c),c)),c) = mult(b,c) ),
inference(extension,[status(thm),parent(t68:2)],[equality_2]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t68:2]) ).
cnf(t72,plain,
mult(b,c) = rd(mult(mult(b,c),rd(mult(c,c),c)),c),
inference(lemma_extension,[status(thm),parent(t70:2)],[l17:1]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t70:2]) ).
cnf(t74,plain,
( ld(a,mult(a,a)) != a
| mult(a,ld(a,a)) != ld(a,mult(a,a))
| mult(a,ld(a,a)) = a ),
inference(extension,[status(thm),parent(t68:3)],[equality_3]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t68:3]) ).
cnf(t76,plain,
mult(a,ld(a,a)) = ld(a,mult(a,a)),
inference(extension,[status(thm),parent(t74:2)],[c03]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t74:2]) ).
cnf(t78,plain,
ld(a,mult(a,a)) = a,
inference(extension,[status(thm),parent(t74:3)],[c01]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t74:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP684-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_PEQ_UEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 10:18:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 277.44/277.77 % SZS status Unsatisfiable for theBenchmark
% 277.44/277.77 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------