%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP665-10 : 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 : n026.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 08:42:13 AM UTC 2026
% Result : Unsatisfiable 252.85s 253.21s
% Output : Proof 252.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of clauses : 36 ( 25 unt; 0 nHn; 32 RR)
% Number of literals : 55 ( 42 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f02,axiom,
ld(A,mult(A,B)) = B,
file('theBenchmark.p',f02) ).
cnf(f08,axiom,
mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))),
file('theBenchmark.p',f08) ).
cnf(f09,axiom,
mult(op_c,A) = mult(A,op_c),
file('theBenchmark.p',f09) ).
cnf(goal,negated_conjecture,
mult(op_c,mult(x0,x1)) != mult(mult(op_c,x0),x1),
file('theBenchmark.p',goal) ).
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,
( ld(Eq_x_0,Eq_x_1) = ld(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,
( 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_c,mult(x0,x1)) != mult(mult(op_c,x0),x1),
inference(start,[status(thm),parent(0:0)],[goal]) ).
cnf(t2,plain,
( mult(mult(x0,x1),op_c) != mult(mult(op_c,x0),x1)
| mult(op_c,mult(x0,x1)) != mult(mult(x0,x1),op_c)
| mult(op_c,mult(x0,x1)) = mult(mult(op_c,x0),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_c,mult(x0,x1)) = mult(mult(x0,x1),op_c),
inference(extension,[status(thm),parent(t2:2)],[f09]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( mult(mult(x0,op_c),ld(op_c,mult(x1,op_c))) != mult(mult(op_c,x0),x1)
| mult(mult(x0,x1),op_c) != mult(mult(x0,op_c),ld(op_c,mult(x1,op_c)))
| mult(mult(x0,x1),op_c) = mult(mult(op_c,x0),x1) ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
mult(mult(x0,x1),op_c) = mult(mult(x0,op_c),ld(op_c,mult(x1,op_c))),
inference(extension,[status(thm),parent(t6:2)],[f08]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( mult(mult(op_c,x0),x1) != mult(mult(x0,op_c),ld(op_c,mult(x1,op_c)))
| mult(mult(x0,op_c),ld(op_c,mult(x1,op_c))) = mult(mult(op_c,x0),x1) ),
inference(extension,[status(thm),parent(t6:3)],[equality_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( mult(op_c,x0) != mult(x0,op_c)
| x1 != ld(op_c,mult(x1,op_c))
| mult(mult(op_c,x0),x1) = mult(mult(x0,op_c),ld(op_c,mult(x1,op_c))) ),
inference(extension,[status(thm),parent(t10:2)],[equality_5]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ld(op_c,mult(op_c,x1)) != ld(op_c,mult(x1,op_c))
| x1 != ld(op_c,mult(op_c,x1))
| x1 = ld(op_c,mult(x1,op_c)) ),
inference(extension,[status(thm),parent(t12:2)],[equality_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ld(op_c,mult(op_c,x1)) != x1
| x1 = ld(op_c,mult(op_c,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,
ld(op_c,mult(op_c,x1)) = x1,
inference(extension,[status(thm),parent(t16:2)],[f02]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( op_c != op_c
| mult(op_c,x1) != mult(x1,op_c)
| ld(op_c,mult(op_c,x1)) = ld(op_c,mult(x1,op_c)) ),
inference(extension,[status(thm),parent(t14:3)],[equality_4]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:3]) ).
cnf(t22,plain,
mult(op_c,x1) = mult(x1,op_c),
inference(extension,[status(thm),parent(t20:2)],[f09]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
op_c = op_c,
inference(extension,[status(thm),parent(t20:3)],[equality_1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
mult(op_c,x0) = mult(x0,op_c),
inference(extension,[status(thm),parent(t12:3)],[f09]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t12:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP665-10 : 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
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 10:15:05 UTC 2026
% 0.09/0.37 % CPUTime :
% 252.85/253.21 % SZS status Unsatisfiable for theBenchmark
% 252.85/253.21 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------