%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP001-1 : TPTP v9.3.1. Released v1.0.0.
% 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 08:41:04 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.42s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 89 ( 74 unt; 0 nHn; 85 RR)
% Number of literals : 134 ( 0 equ; 47 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X),
file('GRP003-0.ax',left_identity) ).
cnf(right_identity,axiom,
product(X,identity,X),
file('GRP003-0.ax',right_identity) ).
cnf(total_function1,axiom,
product(X,Y,multiply(X,Y)),
file('GRP003-0.ax',total_function1) ).
cnf(associativity1,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('GRP003-0.ax',associativity1) ).
cnf(associativity2,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('GRP003-0.ax',associativity2) ).
cnf(square_element,hypothesis,
product(X,X,identity),
file('theBenchmark.p',square_element) ).
cnf(a_times_b_is_c,negated_conjecture,
product(a,b,c),
file('theBenchmark.p',a_times_b_is_c) ).
cnf(prove_b_times_a_is_c,negated_conjecture,
~ product(b,a,c),
file('theBenchmark.p',prove_b_times_a_is_c) ).
cnf(t1,plain,
~ product(b,a,c),
inference(start,[status(thm),parent(0:0)],[prove_b_times_a_is_c]) ).
cnf(t2,plain,
( ~ product(b,multiply(b,multiply(c,b)),a)
| ~ product(identity,multiply(b,multiply(c,b)),c)
| ~ product(b,b,identity)
| product(b,a,c) ),
inference(extension,[status(thm),parent(t1:1)],[associativity1]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
product(b,b,identity),
inference(extension,[status(thm),parent(t2:2)],[square_element]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ product(a,multiply(b,multiply(c,b)),b)
| ~ product(a,b,c)
| ~ product(a,a,identity)
| product(identity,multiply(b,multiply(c,b)),c) ),
inference(extension,[status(thm),parent(t2:3)],[associativity2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
product(a,a,identity),
inference(extension,[status(thm),parent(t6:2)],[square_element]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
product(a,b,c),
inference(extension,[status(thm),parent(t6:3)],[a_times_b_is_c]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( ~ product(b,multiply(b,multiply(c,b)),multiply(c,b))
| ~ product(c,multiply(c,b),b)
| ~ product(c,b,a)
| product(a,multiply(b,multiply(c,b)),b) ),
inference(extension,[status(thm),parent(t6:4)],[associativity2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t6:4]) ).
cnf(t14,plain,
( ~ product(b,b,identity)
| ~ product(a,identity,a)
| ~ product(a,b,c)
| product(c,b,a) ),
inference(extension,[status(thm),parent(t12:2)],[associativity2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
product(a,b,c),
inference(extension,[status(thm),parent(t14:2)],[a_times_b_is_c]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
product(a,identity,a),
inference(extension,[status(thm),parent(t14:3)],[right_identity]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
product(b,b,identity),
inference(extension,[status(thm),parent(t14:4)],[square_element]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:4]) ).
cnf(t22,plain,
( ~ product(c,b,multiply(c,b))
| ~ product(identity,b,b)
| ~ product(c,c,identity)
| product(c,multiply(c,b),b) ),
inference(extension,[status(thm),parent(t12:3)],[associativity1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t12:3]) ).
cnf(t24,plain,
product(c,c,identity),
inference(extension,[status(thm),parent(t22:2)],[square_element]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
product(identity,b,b),
inference(extension,[status(thm),parent(t22:3)],[left_identity]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
cnf(t28,plain,
product(c,b,multiply(c,b)),
inference(extension,[status(thm),parent(t22:4)],[total_function1]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t22:4]) ).
cnf(t30,plain,
( ~ product(b,multiply(c,b),multiply(b,multiply(c,b)))
| ~ product(identity,multiply(c,b),multiply(c,b))
| ~ product(b,b,identity)
| product(b,multiply(b,multiply(c,b)),multiply(c,b)) ),
inference(extension,[status(thm),parent(t12:4)],[associativity1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t12:4]) ).
cnf(t32,plain,
product(b,b,identity),
inference(extension,[status(thm),parent(t30:2)],[square_element]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
product(identity,multiply(c,b),multiply(c,b)),
inference(extension,[status(thm),parent(t30:3)],[left_identity]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t30:3]) ).
cnf(t36,plain,
product(b,multiply(c,b),multiply(b,multiply(c,b))),
inference(extension,[status(thm),parent(t30:4)],[total_function1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t30:4]) ).
cnf(t38,plain,
( ~ product(multiply(b,multiply(c,b)),multiply(b,multiply(c,b)),identity)
| ~ product(a,identity,a)
| ~ product(a,multiply(b,multiply(c,b)),b)
| product(b,multiply(b,multiply(c,b)),a) ),
inference(extension,[status(thm),parent(t2:4)],[associativity2]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t2:4]) ).
cnf(t40,plain,
( ~ product(b,multiply(c,b),multiply(b,multiply(c,b)))
| ~ product(c,multiply(c,b),b)
| ~ product(a,b,c)
| product(a,multiply(b,multiply(c,b)),b) ),
inference(extension,[status(thm),parent(t38:2)],[associativity1]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
product(a,b,c),
inference(extension,[status(thm),parent(t40:2)],[a_times_b_is_c]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( ~ product(c,b,multiply(c,b))
| ~ product(identity,b,b)
| ~ product(c,c,identity)
| product(c,multiply(c,b),b) ),
inference(extension,[status(thm),parent(t40:3)],[associativity1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t40:3]) ).
cnf(t46,plain,
product(c,c,identity),
inference(extension,[status(thm),parent(t44:2)],[square_element]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
product(identity,b,b),
inference(extension,[status(thm),parent(t44:3)],[left_identity]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t44:3]) ).
cnf(t50,plain,
product(c,b,multiply(c,b)),
inference(extension,[status(thm),parent(t44:4)],[total_function1]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t44:4]) ).
cnf(t52,plain,
product(b,multiply(c,b),multiply(b,multiply(c,b))),
inference(extension,[status(thm),parent(t40:4)],[total_function1]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t40:4]) ).
cnf(t54,plain,
( ~ product(b,identity,b)
| ~ product(c,b,a)
| ~ product(c,b,a)
| product(a,identity,a) ),
inference(extension,[status(thm),parent(t38:3)],[associativity2]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t38:3]) ).
cnf(t56,plain,
( ~ product(b,b,identity)
| ~ product(a,identity,a)
| ~ product(a,b,c)
| product(c,b,a) ),
inference(extension,[status(thm),parent(t54:2)],[associativity2]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
product(a,b,c),
inference(extension,[status(thm),parent(t56:2)],[a_times_b_is_c]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t56:2]) ).
cnf(t60,plain,
product(a,identity,a),
inference(extension,[status(thm),parent(t56:3)],[right_identity]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t56:3]) ).
cnf(t62,plain,
product(b,b,identity),
inference(extension,[status(thm),parent(t56:4)],[square_element]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t56:4]) ).
cnf(t64,plain,
( ~ product(b,b,identity)
| ~ product(a,identity,a)
| ~ product(a,b,c)
| product(c,b,a) ),
inference(extension,[status(thm),parent(t54:3)],[associativity2]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t54:3]) ).
cnf(t66,plain,
product(a,b,c),
inference(extension,[status(thm),parent(t64:2)],[a_times_b_is_c]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(t68,plain,
product(a,identity,a),
inference(extension,[status(thm),parent(t64:3)],[right_identity]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t64:3]) ).
cnf(t70,plain,
product(b,b,identity),
inference(extension,[status(thm),parent(t64:4)],[square_element]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t64:4]) ).
cnf(t72,plain,
( ~ product(identity,identity,identity)
| ~ product(b,identity,b)
| ~ product(b,identity,b)
| product(b,identity,b) ),
inference(extension,[status(thm),parent(t54:4)],[associativity2]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t54:4]) ).
cnf(t74,plain,
product(b,identity,b),
inference(extension,[status(thm),parent(t72:2)],[right_identity]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t72:2]) ).
cnf(t76,plain,
product(b,identity,b),
inference(extension,[status(thm),parent(t72:3)],[right_identity]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t72:3]) ).
cnf(t78,plain,
product(identity,identity,identity),
inference(extension,[status(thm),parent(t72:4)],[square_element]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t72:4]) ).
cnf(t80,plain,
product(multiply(b,multiply(c,b)),multiply(b,multiply(c,b)),identity),
inference(extension,[status(thm),parent(t38:4)],[square_element]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t38:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n002.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 08:32:15 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------