%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ROB002-1 : 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 : n007.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 08:55:16 AM UTC 2026
% Result : Unsatisfiable 1.77s 2.07s
% Output : Proof 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 35 ( 23 unt; 0 nHn; 32 RR)
% Number of literals : 53 ( 40 equ; 20 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_add,axiom,
add(X,Y) = add(Y,X),
file('ROB001-0.ax',commutativity_of_add) ).
cnf(robbins_axiom,axiom,
negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X,
file('ROB001-0.ax',robbins_axiom) ).
cnf(double_negation,hypothesis,
negate(negate(X)) = X,
file('theBenchmark.p',double_negation) ).
cnf(prove_huntingtons_axiom,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
file('theBenchmark.p',prove_huntingtons_axiom) ).
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,
( add(Eq_x_0,Eq_x_1) = add(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,
( negate(Eq_x_0) = negate(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
inference(start,[status(thm),parent(0:0)],[prove_huntingtons_axiom]) ).
cnf(t2,plain,
( add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))) != b
| add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != add(negate(add(negate(b),a)),negate(add(negate(b),negate(a))))
| add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b ),
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,
( negate(add(negate(a),negate(b))) != negate(add(negate(b),negate(a)))
| negate(add(a,negate(b))) != negate(add(negate(b),a))
| add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))) ),
inference(extension,[status(thm),parent(t2:2)],[equality_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( add(a,negate(b)) != add(negate(b),a)
| negate(add(a,negate(b))) = negate(add(negate(b),a)) ),
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,
add(a,negate(b)) = add(negate(b),a),
inference(extension,[status(thm),parent(t6:2)],[commutativity_of_add]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( add(negate(a),negate(b)) != add(negate(b),negate(a))
| negate(add(negate(a),negate(b))) = negate(add(negate(b),negate(a))) ),
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,
add(negate(a),negate(b)) = add(negate(b),negate(a)),
inference(extension,[status(thm),parent(t10:2)],[commutativity_of_add]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( negate(negate(b)) != b
| add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))) != negate(negate(b))
| add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))) = b ),
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,
( negate(negate(add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))))) != negate(negate(b))
| add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))) != negate(negate(add(negate(add(negate(b),a)),negate(add(negate(b),negate(a))))))
| add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))) = negate(negate(b)) ),
inference(extension,[status(thm),parent(t14:2)],[equality_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( negate(negate(add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))))) != add(negate(add(negate(b),a)),negate(add(negate(b),negate(a))))
| add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))) = negate(negate(add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))))) ),
inference(extension,[status(thm),parent(t16:2)],[equality_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
negate(negate(add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))))) = add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))),
inference(extension,[status(thm),parent(t18:2)],[double_negation]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( negate(add(negate(add(negate(b),a)),negate(add(negate(b),negate(a))))) != negate(b)
| negate(negate(add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))))) = negate(negate(b)) ),
inference(extension,[status(thm),parent(t16:3)],[equality_5]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t16:3]) ).
cnf(t24,plain,
negate(add(negate(add(negate(b),a)),negate(add(negate(b),negate(a))))) = negate(b),
inference(extension,[status(thm),parent(t22:2)],[robbins_axiom]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
negate(negate(b)) = b,
inference(extension,[status(thm),parent(t14:3)],[double_negation]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t14:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB002-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 19 20:55:52 UTC 2026
% 0.10/0.38 % CPUTime :
% 1.77/2.07 % SZS status Unsatisfiable for theBenchmark
% 1.77/2.07 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------