%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ROB021-1 : 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 : 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 08:55:18 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of clauses : 24 ( 15 unt; 0 nHn; 22 RR)
% Number of literals : 37 ( 29 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 15 ( 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(negative_equality_implies_positive_equality,hypothesis,
( X = Y
| negate(X) != negate(Y) ),
file('theBenchmark.p',negative_equality_implies_positive_equality) ).
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_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(add(negate(add(negate(b),a)),negate(add(negate(b),negate(a))))) != negate(b)
| add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))) = b ),
inference(extension,[status(thm),parent(t2:3)],[negative_equality_implies_positive_equality]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:3]) ).
cnf(t16,plain,
negate(add(negate(add(negate(b),a)),negate(add(negate(b),negate(a))))) = negate(b),
inference(extension,[status(thm),parent(t14:2)],[robbins_axiom]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ROB021-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_PEQ_NUE 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
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 21:01:57 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.21/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.49 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------