%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ROB016-1 : 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 : n011.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 246.21s 266.97s
% Output : Proof 246.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of clauses : 31 ( 20 unt; 0 nHn; 29 RR)
% Number of literals : 48 ( 34 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(robbins_axiom,axiom,
negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X,
file('ROB001-0.ax',robbins_axiom) ).
cnf(condition,hypothesis,
negate(add(d,e)) = negate(e),
file('theBenchmark.p',condition) ).
cnf(k_positive,axiom,
positive_integer(k),
file('theBenchmark.p',k_positive) ).
cnf(lemma_3_6,axiom,
( negate(add(Y,multiply(Vk,add(X,negate(add(X,negate(Y))))))) = negate(Y)
| ~ positive_integer(Vk)
| negate(add(negate(Y),negate(add(X,negate(Y))))) != X ),
file('theBenchmark.p',lemma_3_6) ).
cnf(prove_result,negated_conjecture,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
file('theBenchmark.p',prove_result) ).
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,
( 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,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
inference(start,[status(thm),parent(0:0)],[prove_result]) ).
cnf(t2,plain,
( ~ positive_integer(k)
| negate(add(negate(e),negate(add(d,negate(e))))) != d
| negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) = negate(e) ),
inference(extension,[status(thm),parent(t1:1)],[lemma_3_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( negate(add(negate(e),negate(add(d,negate(e))))) != negate(add(negate(add(d,e)),negate(add(d,negate(e)))))
| negate(add(negate(add(d,e)),negate(add(d,negate(e))))) != d
| negate(add(negate(e),negate(add(d,negate(e))))) = d ),
inference(extension,[status(thm),parent(t2:2)],[equality_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
negate(add(negate(add(d,e)),negate(add(d,negate(e))))) = d,
inference(extension,[status(thm),parent(t4:2)],[robbins_axiom]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( add(negate(e),negate(add(d,negate(e)))) != add(negate(add(d,e)),negate(add(d,negate(e))))
| negate(add(negate(e),negate(add(d,negate(e))))) = negate(add(negate(add(d,e)),negate(add(d,negate(e))))) ),
inference(extension,[status(thm),parent(t4:3)],[equality_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( negate(add(d,negate(e))) != negate(add(d,negate(e)))
| negate(e) != negate(add(d,e))
| add(negate(e),negate(add(d,negate(e)))) = add(negate(add(d,e)),negate(add(d,negate(e)))) ),
inference(extension,[status(thm),parent(t8:2)],[equality_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( negate(add(d,e)) != negate(e)
| negate(e) = negate(add(d,e)) ),
inference(extension,[status(thm),parent(t10:2)],[equality_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
negate(add(d,e)) = negate(e),
inference(extension,[status(thm),parent(t12:2)],[condition]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( add(d,negate(e)) != add(d,negate(e))
| negate(add(d,negate(e))) = negate(add(d,negate(e))) ),
inference(extension,[status(thm),parent(t10:3)],[equality_5]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:3]) ).
cnf(t18,plain,
add(d,negate(e)) = add(d,negate(e)),
inference(extension,[status(thm),parent(t16:2)],[equality_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
positive_integer(k),
inference(extension,[status(thm),parent(t2:3)],[k_positive]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ROB016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.02 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.03/20.82 % CPULimit : 300
% 0.03/20.82 % WCLimit : 300
% 0.03/20.82 % DateTime : Sat Sep 19 21:01:05 UTC 2026
% 0.03/20.82 % CPUTime :
% 246.21/266.97 % SZS status Unsatisfiable for theBenchmark
% 246.21/266.97 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------