%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP702+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 : n010.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 : Theorem 240.66s 240.91s
% Output : Proof 240.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 199 ( 142 unt; 0 def)
% Number of atoms : 307 ( 229 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 225 ( 117 ~; 104 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 40 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f02,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('theBenchmark.p',f02) ).
fof(f08,axiom,
! [B,A] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
file('theBenchmark.p',f08) ).
fof(f09,axiom,
! [B,A] : mult(A,mult(B,op_c)) = mult(mult(A,B),op_c),
file('theBenchmark.p',f09) ).
fof(f10,axiom,
! [B,A] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
file('theBenchmark.p',f10) ).
fof(f11,axiom,
! [A] : op_d = ld(A,mult(op_c,A)),
file('theBenchmark.p',f11) ).
fof(goals,conjecture,
! [X0,X1] :
( mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1)
& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d)
& mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1) ),
file('theBenchmark.p',goals) ).
fof(f_2_1,plain,
! [B,A] : ld(A,mult(A,B)) = B,
inference(fof_nnf,[status(thm)],[f02]) ).
fof(f_2_2,plain,
! [U_3,U_2] : ld(U_2,mult(U_2,U_3)) = U_3,
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_2] : ld(U_2,mult(U_2,U_3)) = U_3,
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
ld(U_2,mult(U_2,U_3)) = U_3,
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_8_1,plain,
! [B,A] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(fof_nnf,[status(thm)],[f08]) ).
fof(f_8_2,plain,
! [U_14,U_13] : mult(op_c,mult(U_13,U_14)) = mult(mult(op_c,U_13),U_14),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_13,U_14] : mult(op_c,mult(U_13,U_14)) = mult(mult(op_c,U_13),U_14),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
mult(op_c,mult(U_13,U_14)) = mult(mult(op_c,U_13),U_14),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [B,A] : mult(A,mult(B,op_c)) = mult(mult(A,B),op_c),
inference(fof_nnf,[status(thm)],[f09]) ).
fof(f_9_2,plain,
! [U_16,U_15] : mult(U_15,mult(U_16,op_c)) = mult(mult(U_15,U_16),op_c),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_15,U_16] : mult(U_15,mult(U_16,op_c)) = mult(mult(U_15,U_16),op_c),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
mult(U_15,mult(U_16,op_c)) = mult(mult(U_15,U_16),op_c),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [B,A] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(fof_nnf,[status(thm)],[f10]) ).
fof(f_10_2,plain,
! [U_18,U_17] : mult(U_17,mult(op_c,U_18)) = mult(mult(U_17,op_c),U_18),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_17,U_18] : mult(U_17,mult(op_c,U_18)) = mult(mult(U_17,op_c),U_18),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
mult(U_17,mult(op_c,U_18)) = mult(mult(U_17,op_c),U_18),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A] : op_d = ld(A,mult(op_c,A)),
inference(fof_nnf,[status(thm)],[f11]) ).
fof(f_11_2,plain,
! [U_19] : op_d = ld(U_19,mult(op_c,U_19)),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_19] : op_d = ld(U_19,mult(op_c,U_19)),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
op_d = ld(U_19,mult(op_c,U_19)),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_14_1,negated_conjecture,
~ ! [X0,X1] :
( mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1)
& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d)
& mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1) ),
inference(negate,[status(cth)],[goals]) ).
fof(f_14_2,negated_conjecture,
? [X0,X1] :
( mult(X0,mult(op_d,X1)) != mult(mult(X0,op_d),X1)
| mult(X0,mult(X1,op_d)) != mult(mult(X0,X1),op_d)
| mult(op_d,mult(X0,X1)) != mult(mult(op_d,X0),X1) ),
inference(fof_nnf,[status(thm)],[f_14_1]) ).
fof(f_14_3,negated_conjecture,
? [U_25,U_24] :
( mult(U_25,mult(op_d,U_24)) != mult(mult(U_25,op_d),U_24)
| mult(U_25,mult(U_24,op_d)) != mult(mult(U_25,U_24),op_d)
| mult(op_d,mult(U_25,U_24)) != mult(mult(op_d,U_25),U_24) ),
inference(variable_rename,[status(thm)],[f_14_2]) ).
fof(f_14_4,negated_conjecture,
( ? [U_31,U_28] : mult(U_31,mult(op_d,U_28)) != mult(mult(U_31,op_d),U_28)
| ? [U_30,U_27] : mult(U_30,mult(U_27,op_d)) != mult(mult(U_30,U_27),op_d)
| ? [U_29,U_26] : mult(op_d,mult(U_29,U_26)) != mult(mult(op_d,U_29),U_26) ),
inference(miniscope,[status(thm)],[f_14_3]) ).
fof(f_14_5,negated_conjecture,
( ? [U_31,U_28] : mult(U_31,mult(op_d,U_28)) != mult(mult(U_31,op_d),U_28)
| ? [U_30,U_27] : mult(U_30,mult(U_27,op_d)) != mult(mult(U_30,U_27),op_d)
| ? [U_26] : mult(op_d,mult(sK1,U_26)) != mult(mult(op_d,sK1),U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_29,sK1)],[f_14_4]) ).
fof(f_14_6,negated_conjecture,
( ? [U_31,U_28] : mult(U_31,mult(op_d,U_28)) != mult(mult(U_31,op_d),U_28)
| ? [U_30,U_27] : mult(U_30,mult(U_27,op_d)) != mult(mult(U_30,U_27),op_d)
| mult(op_d,mult(sK1,sK2)) != mult(mult(op_d,sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_26,sK2)],[f_14_5]) ).
fof(f_14_7,negated_conjecture,
( ? [U_31,U_28] : mult(U_31,mult(op_d,U_28)) != mult(mult(U_31,op_d),U_28)
| ? [U_27] : mult(sK3,mult(U_27,op_d)) != mult(mult(sK3,U_27),op_d)
| mult(op_d,mult(sK1,sK2)) != mult(mult(op_d,sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_30,sK3)],[f_14_6]) ).
fof(f_14_8,negated_conjecture,
( ? [U_31,U_28] : mult(U_31,mult(op_d,U_28)) != mult(mult(U_31,op_d),U_28)
| mult(sK3,mult(sK4,op_d)) != mult(mult(sK3,sK4),op_d)
| mult(op_d,mult(sK1,sK2)) != mult(mult(op_d,sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_27,sK4)],[f_14_7]) ).
fof(f_14_9,negated_conjecture,
( ? [U_28] : mult(sK5,mult(op_d,U_28)) != mult(mult(sK5,op_d),U_28)
| mult(sK3,mult(sK4,op_d)) != mult(mult(sK3,sK4),op_d)
| mult(op_d,mult(sK1,sK2)) != mult(mult(op_d,sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_31,sK5)],[f_14_8]) ).
fof(f_14_10,negated_conjecture,
( mult(sK5,mult(op_d,sK6)) != mult(mult(sK5,op_d),sK6)
| mult(sK3,mult(sK4,op_d)) != mult(mult(sK3,sK4),op_d)
| mult(op_d,mult(sK1,sK2)) != mult(mult(op_d,sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_28,sK6)],[f_14_9]) ).
fof(f_14_11,negated_conjecture,
( mult(sK5,mult(op_d,sK6)) != mult(mult(sK5,op_d),sK6)
| mult(sK3,mult(sK4,op_d)) != mult(mult(sK3,sK4),op_d)
| mult(op_d,mult(sK1,sK2)) != mult(mult(op_d,sK1),sK2) ),
inference(definitional_conversion,[status(esa)],[f_14_10]) ).
cnf(f_14_12,negated_conjecture,
( mult(sK5,mult(op_d,sK6)) != mult(mult(sK5,op_d),sK6)
| mult(sK3,mult(sK4,op_d)) != mult(mult(sK3,sK4),op_d)
| mult(op_d,mult(sK1,sK2)) != mult(mult(op_d,sK1),sK2) ),
inference(clausify,[status(thm)],[f_14_11]) ).
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_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(op_d,mult(sK1,sK2)) != mult(mult(op_d,sK1),sK2)
| mult(sK3,mult(sK4,op_d)) != mult(mult(sK3,sK4),op_d)
| mult(sK5,mult(op_d,sK6)) != mult(mult(sK5,op_d),sK6) ),
inference(start,[status(thm),parent(0:0)],[f_14_12]) ).
cnf(t2,plain,
( mult(sK5,mult(ld(op_c,mult(op_c,op_c)),sK6)) != mult(mult(sK5,op_d),sK6)
| mult(sK5,mult(op_d,sK6)) != mult(sK5,mult(ld(op_c,mult(op_c,op_c)),sK6))
| mult(sK5,mult(op_d,sK6)) = mult(mult(sK5,op_d),sK6) ),
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,
( sK5 != sK5
| mult(op_d,sK6) != mult(ld(op_c,mult(op_c,op_c)),sK6)
| mult(sK5,mult(op_d,sK6)) = mult(sK5,mult(ld(op_c,mult(op_c,op_c)),sK6)) ),
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,
( op_d != ld(op_c,mult(op_c,op_c))
| sK6 != sK6
| mult(op_d,sK6) = mult(ld(op_c,mult(op_c,op_c)),sK6) ),
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,
sK6 = sK6,
inference(extension,[status(thm),parent(t6:2)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
op_d = ld(op_c,mult(op_c,op_c)),
inference(extension,[status(thm),parent(t6:3)],[f_11_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
sK5 = sK5,
inference(extension,[status(thm),parent(t4:3)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
( mult(sK5,mult(op_c,sK6)) != mult(mult(sK5,op_d),sK6)
| mult(sK5,mult(ld(op_c,mult(op_c,op_c)),sK6)) != mult(sK5,mult(op_c,sK6))
| mult(sK5,mult(ld(op_c,mult(op_c,op_c)),sK6)) = mult(mult(sK5,op_d),sK6) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:3]) ).
cnf(t16,plain,
( sK5 != sK5
| mult(ld(op_c,mult(op_c,op_c)),sK6) != mult(op_c,sK6)
| mult(sK5,mult(ld(op_c,mult(op_c,op_c)),sK6)) = mult(sK5,mult(op_c,sK6)) ),
inference(extension,[status(thm),parent(t14:2)],[equality_5]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ld(op_c,mult(op_c,op_c)) != op_c
| sK6 != sK6
| mult(ld(op_c,mult(op_c,op_c)),sK6) = mult(op_c,sK6) ),
inference(extension,[status(thm),parent(t16:2)],[equality_5]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
sK6 = sK6,
inference(extension,[status(thm),parent(t18:2)],[equality_1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
ld(op_c,mult(op_c,op_c)) = op_c,
inference(extension,[status(thm),parent(t18:3)],[f_2_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
sK5 = sK5,
inference(extension,[status(thm),parent(t16:3)],[equality_1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t16:3]) ).
cnf(t26,plain,
( mult(mult(sK5,op_d),sK6) != mult(sK5,mult(op_c,sK6))
| mult(sK5,mult(op_c,sK6)) = mult(mult(sK5,op_d),sK6) ),
inference(extension,[status(thm),parent(t14:3)],[equality_2]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t14:3]) ).
cnf(t28,plain,
( mult(mult(sK5,ld(op_c,mult(op_c,op_c))),sK6) != mult(sK5,mult(op_c,sK6))
| mult(mult(sK5,op_d),sK6) != mult(mult(sK5,ld(op_c,mult(op_c,op_c))),sK6)
| mult(mult(sK5,op_d),sK6) = mult(sK5,mult(op_c,sK6)) ),
inference(extension,[status(thm),parent(t26:2)],[equality_3]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( mult(sK5,op_d) != mult(sK5,ld(op_c,mult(op_c,op_c)))
| sK6 != sK6
| mult(mult(sK5,op_d),sK6) = mult(mult(sK5,ld(op_c,mult(op_c,op_c))),sK6) ),
inference(extension,[status(thm),parent(t28:2)],[equality_5]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
sK6 = sK6,
inference(extension,[status(thm),parent(t30:2)],[equality_1]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
( sK5 != sK5
| op_d != ld(op_c,mult(op_c,op_c))
| mult(sK5,op_d) = mult(sK5,ld(op_c,mult(op_c,op_c))) ),
inference(extension,[status(thm),parent(t30:3)],[equality_5]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t30:3]) ).
cnf(t36,plain,
op_d = ld(op_c,mult(op_c,op_c)),
inference(extension,[status(thm),parent(t34:2)],[f_11_4]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
sK5 = sK5,
inference(extension,[status(thm),parent(t34:3)],[equality_1]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t34:3]) ).
cnf(t40,plain,
( mult(mult(sK5,op_c),sK6) != mult(sK5,mult(op_c,sK6))
| mult(mult(sK5,ld(op_c,mult(op_c,op_c))),sK6) != mult(mult(sK5,op_c),sK6)
| mult(mult(sK5,ld(op_c,mult(op_c,op_c))),sK6) = mult(sK5,mult(op_c,sK6)) ),
inference(extension,[status(thm),parent(t28:3)],[equality_3]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t28:3]) ).
cnf(t42,plain,
( mult(sK5,ld(op_c,mult(op_c,op_c))) != mult(sK5,op_c)
| sK6 != sK6
| mult(mult(sK5,ld(op_c,mult(op_c,op_c))),sK6) = mult(mult(sK5,op_c),sK6) ),
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,
sK6 = sK6,
inference(extension,[status(thm),parent(t42:2)],[equality_1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
( sK5 != sK5
| ld(op_c,mult(op_c,op_c)) != op_c
| mult(sK5,ld(op_c,mult(op_c,op_c))) = mult(sK5,op_c) ),
inference(extension,[status(thm),parent(t42:3)],[equality_5]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t42:3]) ).
cnf(t48,plain,
ld(op_c,mult(op_c,op_c)) = op_c,
inference(extension,[status(thm),parent(t46:2)],[f_2_4]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
sK5 = sK5,
inference(extension,[status(thm),parent(t46:3)],[equality_1]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t46:3]) ).
cnf(t52,plain,
( mult(sK5,mult(op_c,sK6)) != mult(mult(sK5,op_c),sK6)
| mult(mult(sK5,op_c),sK6) = mult(sK5,mult(op_c,sK6)) ),
inference(extension,[status(thm),parent(t40:3)],[equality_2]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t40:3]) ).
cnf(t54,plain,
( mult(mult(sK5,op_c),sK6) != mult(mult(sK5,op_c),sK6)
| mult(sK5,mult(op_c,sK6)) != mult(mult(sK5,op_c),sK6)
| mult(sK5,mult(op_c,sK6)) = mult(mult(sK5,op_c),sK6) ),
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,
mult(sK5,mult(op_c,sK6)) = mult(mult(sK5,op_c),sK6),
inference(extension,[status(thm),parent(t54:2)],[f_10_4]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
mult(mult(sK5,op_c),sK6) = mult(mult(sK5,op_c),sK6),
inference(extension,[status(thm),parent(t54:3)],[equality_1]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t54:3]) ).
cnf(t60,plain,
( mult(sK3,mult(sK4,ld(op_c,mult(op_c,op_c)))) != mult(mult(sK3,sK4),op_d)
| mult(sK3,mult(sK4,op_d)) != mult(sK3,mult(sK4,ld(op_c,mult(op_c,op_c))))
| mult(sK3,mult(sK4,op_d)) = mult(mult(sK3,sK4),op_d) ),
inference(extension,[status(thm),parent(t1:2)],[equality_3]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t1:2]) ).
cnf(t62,plain,
( sK3 != sK3
| mult(sK4,op_d) != mult(sK4,ld(op_c,mult(op_c,op_c)))
| mult(sK3,mult(sK4,op_d)) = mult(sK3,mult(sK4,ld(op_c,mult(op_c,op_c)))) ),
inference(extension,[status(thm),parent(t60:2)],[equality_5]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t60:2]) ).
cnf(t64,plain,
( sK4 != sK4
| op_d != ld(op_c,mult(op_c,op_c))
| mult(sK4,op_d) = mult(sK4,ld(op_c,mult(op_c,op_c))) ),
inference(extension,[status(thm),parent(t62:2)],[equality_5]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t62:2]) ).
cnf(t66,plain,
op_d = ld(op_c,mult(op_c,op_c)),
inference(extension,[status(thm),parent(t64:2)],[f_11_4]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(t68,plain,
sK4 = sK4,
inference(extension,[status(thm),parent(t64:3)],[equality_1]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t64:3]) ).
cnf(t70,plain,
sK3 = sK3,
inference(extension,[status(thm),parent(t62:3)],[equality_1]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t62:3]) ).
cnf(t72,plain,
( mult(sK3,mult(sK4,op_c)) != mult(mult(sK3,sK4),op_d)
| mult(sK3,mult(sK4,ld(op_c,mult(op_c,op_c)))) != mult(sK3,mult(sK4,op_c))
| mult(sK3,mult(sK4,ld(op_c,mult(op_c,op_c)))) = mult(mult(sK3,sK4),op_d) ),
inference(extension,[status(thm),parent(t60:3)],[equality_3]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t60:3]) ).
cnf(t74,plain,
( sK3 != sK3
| mult(sK4,ld(op_c,mult(op_c,op_c))) != mult(sK4,op_c)
| mult(sK3,mult(sK4,ld(op_c,mult(op_c,op_c)))) = mult(sK3,mult(sK4,op_c)) ),
inference(extension,[status(thm),parent(t72:2)],[equality_5]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t72:2]) ).
cnf(t76,plain,
( sK4 != sK4
| ld(op_c,mult(op_c,op_c)) != op_c
| mult(sK4,ld(op_c,mult(op_c,op_c))) = mult(sK4,op_c) ),
inference(extension,[status(thm),parent(t74:2)],[equality_5]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t74:2]) ).
cnf(t78,plain,
ld(op_c,mult(op_c,op_c)) = op_c,
inference(extension,[status(thm),parent(t76:2)],[f_2_4]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t76:2]) ).
cnf(t80,plain,
sK4 = sK4,
inference(extension,[status(thm),parent(t76:3)],[equality_1]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t76:3]) ).
cnf(t82,plain,
sK3 = sK3,
inference(extension,[status(thm),parent(t74:3)],[equality_1]) ).
cnf(t83,plain,
$false,
inference(connection,[status(thm),parent(t82:1)],[t82:1,t74:3]) ).
cnf(t84,plain,
( mult(mult(sK3,sK4),op_c) != mult(mult(sK3,sK4),op_d)
| mult(sK3,mult(sK4,op_c)) != mult(mult(sK3,sK4),op_c)
| mult(sK3,mult(sK4,op_c)) = mult(mult(sK3,sK4),op_d) ),
inference(extension,[status(thm),parent(t72:3)],[equality_3]) ).
cnf(t85,plain,
$false,
inference(connection,[status(thm),parent(t84:1)],[t84:1,t72:3]) ).
cnf(t86,plain,
mult(sK3,mult(sK4,op_c)) = mult(mult(sK3,sK4),op_c),
inference(extension,[status(thm),parent(t84:2)],[f_9_4]) ).
cnf(t87,plain,
$false,
inference(connection,[status(thm),parent(t86:1)],[t86:1,t84:2]) ).
cnf(t88,plain,
( mult(sK3,sK4) != mult(sK3,sK4)
| op_c != op_d
| mult(mult(sK3,sK4),op_c) = mult(mult(sK3,sK4),op_d) ),
inference(extension,[status(thm),parent(t84:3)],[equality_5]) ).
cnf(t89,plain,
$false,
inference(connection,[status(thm),parent(t88:1)],[t88:1,t84:3]) ).
cnf(t90,plain,
( op_d != op_c
| op_c = op_d ),
inference(extension,[status(thm),parent(t88:2)],[equality_2]) ).
cnf(t91,plain,
$false,
inference(connection,[status(thm),parent(t90:1)],[t90:1,t88:2]) ).
cnf(t92,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(t90:2)],[equality_3]) ).
cnf(t93,plain,
$false,
inference(connection,[status(thm),parent(t92:1)],[t92:1,t90:2]) ).
cnf(t94,plain,
op_d = ld(op_c,mult(op_c,op_c)),
inference(extension,[status(thm),parent(t92:2)],[f_11_4]) ).
cnf(t95,plain,
$false,
inference(connection,[status(thm),parent(t94:1)],[t94:1,t92:2]) ).
cnf(t96,plain,
ld(op_c,mult(op_c,op_c)) = op_c,
inference(extension,[status(thm),parent(t92:3)],[f_2_4]) ).
cnf(t97,plain,
$false,
inference(connection,[status(thm),parent(t96:1)],[t96:1,t92:3]) ).
cnf(t98,plain,
( sK3 != sK3
| sK4 != sK4
| mult(sK3,sK4) = mult(sK3,sK4) ),
inference(extension,[status(thm),parent(t88:3)],[equality_5]) ).
cnf(t99,plain,
$false,
inference(connection,[status(thm),parent(t98:1)],[t98:1,t88:3]) ).
cnf(t100,plain,
sK4 = sK4,
inference(extension,[status(thm),parent(t98:2)],[equality_1]) ).
cnf(t101,plain,
$false,
inference(connection,[status(thm),parent(t100:1)],[t100:1,t98:2]) ).
cnf(t102,plain,
sK3 = sK3,
inference(extension,[status(thm),parent(t98:3)],[equality_1]) ).
cnf(t103,plain,
$false,
inference(connection,[status(thm),parent(t102:1)],[t102:1,t98:3]) ).
cnf(t104,plain,
( mult(ld(op_c,mult(op_c,op_c)),mult(sK1,sK2)) != mult(mult(op_d,sK1),sK2)
| mult(op_d,mult(sK1,sK2)) != mult(ld(op_c,mult(op_c,op_c)),mult(sK1,sK2))
| mult(op_d,mult(sK1,sK2)) = mult(mult(op_d,sK1),sK2) ),
inference(extension,[status(thm),parent(t1:3)],[equality_3]) ).
cnf(t105,plain,
$false,
inference(connection,[status(thm),parent(t104:1)],[t104:1,t1:3]) ).
cnf(t106,plain,
( op_d != ld(op_c,mult(op_c,op_c))
| mult(sK1,sK2) != mult(sK1,sK2)
| mult(op_d,mult(sK1,sK2)) = mult(ld(op_c,mult(op_c,op_c)),mult(sK1,sK2)) ),
inference(extension,[status(thm),parent(t104:2)],[equality_5]) ).
cnf(t107,plain,
$false,
inference(connection,[status(thm),parent(t106:1)],[t106:1,t104:2]) ).
cnf(t108,plain,
( sK1 != sK1
| sK2 != sK2
| mult(sK1,sK2) = mult(sK1,sK2) ),
inference(extension,[status(thm),parent(t106:2)],[equality_5]) ).
cnf(t109,plain,
$false,
inference(connection,[status(thm),parent(t108:1)],[t108:1,t106:2]) ).
cnf(t110,plain,
sK2 = sK2,
inference(extension,[status(thm),parent(t108:2)],[equality_1]) ).
cnf(t111,plain,
$false,
inference(connection,[status(thm),parent(t110:1)],[t110:1,t108:2]) ).
cnf(t112,plain,
sK1 = sK1,
inference(extension,[status(thm),parent(t108:3)],[equality_1]) ).
cnf(t113,plain,
$false,
inference(connection,[status(thm),parent(t112:1)],[t112:1,t108:3]) ).
cnf(t114,plain,
op_d = ld(op_c,mult(op_c,op_c)),
inference(extension,[status(thm),parent(t106:3)],[f_11_4]) ).
cnf(t115,plain,
$false,
inference(connection,[status(thm),parent(t114:1)],[t114:1,t106:3]) ).
cnf(t116,plain,
( mult(op_c,mult(sK1,sK2)) != mult(mult(op_d,sK1),sK2)
| mult(ld(op_c,mult(op_c,op_c)),mult(sK1,sK2)) != mult(op_c,mult(sK1,sK2))
| mult(ld(op_c,mult(op_c,op_c)),mult(sK1,sK2)) = mult(mult(op_d,sK1),sK2) ),
inference(extension,[status(thm),parent(t104:3)],[equality_3]) ).
cnf(t117,plain,
$false,
inference(connection,[status(thm),parent(t116:1)],[t116:1,t104:3]) ).
cnf(t118,plain,
( ld(op_c,mult(op_c,op_c)) != op_c
| mult(sK1,sK2) != mult(sK1,sK2)
| mult(ld(op_c,mult(op_c,op_c)),mult(sK1,sK2)) = mult(op_c,mult(sK1,sK2)) ),
inference(extension,[status(thm),parent(t116:2)],[equality_5]) ).
cnf(t119,plain,
$false,
inference(connection,[status(thm),parent(t118:1)],[t118:1,t116:2]) ).
cnf(t120,plain,
( sK1 != sK1
| sK2 != sK2
| mult(sK1,sK2) = mult(sK1,sK2) ),
inference(extension,[status(thm),parent(t118:2)],[equality_5]) ).
cnf(t121,plain,
$false,
inference(connection,[status(thm),parent(t120:1)],[t120:1,t118:2]) ).
cnf(t122,plain,
sK2 = sK2,
inference(extension,[status(thm),parent(t120:2)],[equality_1]) ).
cnf(t123,plain,
$false,
inference(connection,[status(thm),parent(t122:1)],[t122:1,t120:2]) ).
cnf(t124,plain,
sK1 = sK1,
inference(extension,[status(thm),parent(t120:3)],[equality_1]) ).
cnf(t125,plain,
$false,
inference(connection,[status(thm),parent(t124:1)],[t124:1,t120:3]) ).
cnf(t126,plain,
ld(op_c,mult(op_c,op_c)) = op_c,
inference(extension,[status(thm),parent(t118:3)],[f_2_4]) ).
cnf(t127,plain,
$false,
inference(connection,[status(thm),parent(t126:1)],[t126:1,t118:3]) ).
cnf(t128,plain,
( mult(mult(op_d,sK1),sK2) != mult(op_c,mult(sK1,sK2))
| mult(op_c,mult(sK1,sK2)) = mult(mult(op_d,sK1),sK2) ),
inference(extension,[status(thm),parent(t116:3)],[equality_2]) ).
cnf(t129,plain,
$false,
inference(connection,[status(thm),parent(t128:1)],[t128:1,t116:3]) ).
cnf(t130,plain,
( mult(mult(ld(op_c,mult(op_c,op_c)),sK1),sK2) != mult(op_c,mult(sK1,sK2))
| mult(mult(op_d,sK1),sK2) != mult(mult(ld(op_c,mult(op_c,op_c)),sK1),sK2)
| mult(mult(op_d,sK1),sK2) = mult(op_c,mult(sK1,sK2)) ),
inference(extension,[status(thm),parent(t128:2)],[equality_3]) ).
cnf(t131,plain,
$false,
inference(connection,[status(thm),parent(t130:1)],[t130:1,t128:2]) ).
cnf(t132,plain,
( mult(op_d,sK1) != mult(ld(op_c,mult(op_c,op_c)),sK1)
| sK2 != sK2
| mult(mult(op_d,sK1),sK2) = mult(mult(ld(op_c,mult(op_c,op_c)),sK1),sK2) ),
inference(extension,[status(thm),parent(t130:2)],[equality_5]) ).
cnf(t133,plain,
$false,
inference(connection,[status(thm),parent(t132:1)],[t132:1,t130:2]) ).
cnf(t134,plain,
sK2 = sK2,
inference(extension,[status(thm),parent(t132:2)],[equality_1]) ).
cnf(t135,plain,
$false,
inference(connection,[status(thm),parent(t134:1)],[t134:1,t132:2]) ).
cnf(t136,plain,
( op_d != ld(op_c,mult(op_c,op_c))
| sK1 != sK1
| mult(op_d,sK1) = mult(ld(op_c,mult(op_c,op_c)),sK1) ),
inference(extension,[status(thm),parent(t132:3)],[equality_5]) ).
cnf(t137,plain,
$false,
inference(connection,[status(thm),parent(t136:1)],[t136:1,t132:3]) ).
cnf(t138,plain,
sK1 = sK1,
inference(extension,[status(thm),parent(t136:2)],[equality_1]) ).
cnf(t139,plain,
$false,
inference(connection,[status(thm),parent(t138:1)],[t138:1,t136:2]) ).
cnf(t140,plain,
op_d = ld(op_c,mult(op_c,op_c)),
inference(extension,[status(thm),parent(t136:3)],[f_11_4]) ).
cnf(t141,plain,
$false,
inference(connection,[status(thm),parent(t140:1)],[t140:1,t136:3]) ).
cnf(t142,plain,
( mult(mult(op_c,sK1),sK2) != mult(op_c,mult(sK1,sK2))
| mult(mult(ld(op_c,mult(op_c,op_c)),sK1),sK2) != mult(mult(op_c,sK1),sK2)
| mult(mult(ld(op_c,mult(op_c,op_c)),sK1),sK2) = mult(op_c,mult(sK1,sK2)) ),
inference(extension,[status(thm),parent(t130:3)],[equality_3]) ).
cnf(t143,plain,
$false,
inference(connection,[status(thm),parent(t142:1)],[t142:1,t130:3]) ).
cnf(t144,plain,
( mult(ld(op_c,mult(op_c,op_c)),sK1) != mult(op_c,sK1)
| sK2 != sK2
| mult(mult(ld(op_c,mult(op_c,op_c)),sK1),sK2) = mult(mult(op_c,sK1),sK2) ),
inference(extension,[status(thm),parent(t142:2)],[equality_5]) ).
cnf(t145,plain,
$false,
inference(connection,[status(thm),parent(t144:1)],[t144:1,t142:2]) ).
cnf(t146,plain,
sK2 = sK2,
inference(extension,[status(thm),parent(t144:2)],[equality_1]) ).
cnf(t147,plain,
$false,
inference(connection,[status(thm),parent(t146:1)],[t146:1,t144:2]) ).
cnf(t148,plain,
( ld(op_c,mult(op_c,op_c)) != op_c
| sK1 != sK1
| mult(ld(op_c,mult(op_c,op_c)),sK1) = mult(op_c,sK1) ),
inference(extension,[status(thm),parent(t144:3)],[equality_5]) ).
cnf(t149,plain,
$false,
inference(connection,[status(thm),parent(t148:1)],[t148:1,t144:3]) ).
cnf(t150,plain,
sK1 = sK1,
inference(extension,[status(thm),parent(t148:2)],[equality_1]) ).
cnf(t151,plain,
$false,
inference(connection,[status(thm),parent(t150:1)],[t150:1,t148:2]) ).
cnf(t152,plain,
ld(op_c,mult(op_c,op_c)) = op_c,
inference(extension,[status(thm),parent(t148:3)],[f_2_4]) ).
cnf(t153,plain,
$false,
inference(connection,[status(thm),parent(t152:1)],[t152:1,t148:3]) ).
cnf(t154,plain,
( mult(op_c,mult(sK1,sK2)) != mult(mult(op_c,sK1),sK2)
| mult(mult(op_c,sK1),sK2) = mult(op_c,mult(sK1,sK2)) ),
inference(extension,[status(thm),parent(t142:3)],[equality_2]) ).
cnf(t155,plain,
$false,
inference(connection,[status(thm),parent(t154:1)],[t154:1,t142:3]) ).
cnf(t156,plain,
mult(op_c,mult(sK1,sK2)) = mult(mult(op_c,sK1),sK2),
inference(extension,[status(thm),parent(t154:2)],[f_8_4]) ).
cnf(t157,plain,
$false,
inference(connection,[status(thm),parent(t156:1)],[t156:1,t154:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP702+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_PEQ 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
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 10:21:38 UTC 2026
% 0.09/0.37 % CPUTime :
% 240.66/240.91 % SZS status Theorem for theBenchmark
% 240.66/240.91 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------