%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ROB016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:39:36 PM UTC 2026
% Result : Unsatisfiable 80.31s 11.81s
% Output : Proof 80.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 46 unt; 0 def)
% Number of atoms : 58 ( 50 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 58 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,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('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3_6) ).
fof(f9_nnf,plain,
! [Y,X,Vk] :
( 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 ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Y,X,Vk] :
( 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 ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( negate(add(X0,multiply(X2,add(X1,negate(add(X1,negate(X0))))))) = negate(X0)
| ~ positive_integer(X2)
| negate(add(negate(X0),negate(add(X1,negate(X0))))) != X1 ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t10,plain,
ifeq(negate(add(negate(X1),negate(add(X2,negate(X1))))),X2,ifeq(positive_integer(X3),true,negate(add(X1,multiply(X3,add(X2,negate(add(X2,negate(X1))))))),negate(X1)),negate(X1)) = negate(X1),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t100,plain,
ifeq(negate(add(negate(X1),negate(add(X2,negate(X1))))),X2,ifeq(positive_integer(X3),true,negate(add(X1,multiply(X3,add(X2,negate(add(X2,negate(X1))))))),negate(X1)),negate(X1)) = negate(X1),
inference(orient,[status(thm)],[t10]) ).
cnf(f8,axiom,
positive_integer(k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_positive) ).
fof(f8_nnf,plain,
positive_integer(k),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
positive_integer(k),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(t0,plain,
positive_integer(k) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t11,plain,
positive_integer(k) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t101,plain,
negate(X1) = ifeq(negate(add(negate(X1),negate(add(X2,negate(X1))))),X2,ifeq(true,true,negate(add(X1,multiply(k,add(X2,negate(add(X2,negate(X1))))))),negate(X1)),negate(X1)),
inference(cp,[status(thm)],[t100,t11]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t15,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t35951,plain,
negate(X1) = ifeq(negate(add(negate(X1),negate(add(X2,negate(X1))))),X2,negate(add(X1,multiply(k,add(X2,negate(add(X2,negate(X1))))))),negate(X1)),
inference(step,[status(thm)],[t101,t15]) ).
cnf(t2687,plain,
ifeq(negate(add(negate(X1),negate(add(X2,negate(X1))))),X2,negate(add(X1,multiply(k,add(X2,negate(add(X2,negate(X1))))))),negate(X1)) = negate(X1),
inference(orient,[status(thm)],[t35951]) ).
cnf(f2,axiom,
negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',robbins_axiom) ).
fof(f2_nnf,plain,
! [X,Y] : negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
negate(add(negate(add(X0,X1)),negate(add(X0,negate(X1))))) = X0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t8,plain,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t26,plain,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(f0,axiom,
add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f0_nnf,plain,
! [X,Y] : add(X,Y) = add(Y,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] : add(X,Y) = add(Y,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t3,plain,
add(X1,X2) = add(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t17,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t3]) ).
cnf(t29,plain,
X1 = negate(add(negate(add(X2,X1)),negate(add(X1,negate(X2))))),
inference(cp,[status(thm)],[t26,t17]) ).
cnf(t558,plain,
negate(add(negate(add(X1,X2)),negate(add(X2,negate(X1))))) = X2,
inference(orient,[status(thm)],[t29]) ).
cnf(f7,hypothesis,
negate(add(d,e)) = negate(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
fof(f7_nnf,plain,
negate(add(d,e)) = negate(e),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
negate(add(d,e)) = negate(e),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(t5,plain,
negate(add(d,e)) = negate(e),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t14,plain,
negate(add(d,e)) = negate(e),
inference(orient,[status(thm)],[t5]) ).
cnf(t35764,plain,
negate(add(e,d)) = negate(e),
inference(step,[status(thm)],[t14,t17]) ).
cnf(t18,plain,
negate(add(e,d)) = negate(e),
inference(rw,[status(thm)],[t35764]) ).
cnf(t21,plain,
negate(add(e,d)) = negate(e),
inference(orient,[status(thm)],[t18]) ).
cnf(t562,plain,
d = negate(add(negate(e),negate(add(d,negate(e))))),
inference(cp,[status(thm)],[t558,t21]) ).
cnf(t957,plain,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
inference(orient,[status(thm)],[t562]) ).
cnf(t2718,plain,
negate(e) = ifeq(d,d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)),
inference(cp,[status(thm)],[t2687,t957]) ).
cnf(t36771,plain,
negate(e) = negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),
inference(step,[status(thm)],[t2718,t15]) ).
cnf(t35708,plain,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) = negate(e),
inference(orient,[status(thm)],[t36771]) ).
cnf(f10,negated_conjecture,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_result) ).
fof(f10_nnf,plain,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(goal_0,negated_conjecture,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(g0_0,plain,
negate(e) != negate(e),
inference(rw,[status(thm)],[goal_0,t35708]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 08:29:53 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 80.31/11.81 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 80.31/11.81 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------