%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ROB021-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 7.24s 6.65s
% Output : Proof 7.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 29 unt; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 12 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-4 aty)
% Number of variables : 52 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
add(X,Y) = add(Y,X),
file('/export/starexec/sandbox2/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(t0,plain,
add(X1,X2) = add(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t13,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t0]) ).
cnf(f3,hypothesis,
( X = Y
| negate(X) != negate(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',negative_equality_implies_positive_equality) ).
fof(f3_nnf,plain,
! [X,Y] :
( X = Y
| negate(X) != negate(Y) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( X = Y
| negate(X) != negate(Y) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( X0 = X1
| negate(X0) != negate(X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t2,plain,
ifeq(negate(X1),negate(X2),X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t10,plain,
ifeq(negate(X1),negate(X2),X1,X2) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(f2,axiom,
negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X,
file('/export/starexec/sandbox2/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(t4,plain,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t5,plain,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t11,plain,
X1 = ifeq(X2,negate(X1),add(negate(add(X2,X3)),negate(add(X2,negate(X3)))),X1),
inference(cp,[status(thm)],[t10,t5]) ).
cnf(t531,plain,
ifeq(X1,negate(X2),add(negate(add(X1,X3)),negate(add(X1,negate(X3)))),X2) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t1,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t532,plain,
X1 = add(negate(add(negate(X1),X2)),negate(add(negate(X1),negate(X2)))),
inference(cp,[status(thm)],[t531,t9]) ).
cnf(t589,plain,
add(negate(add(negate(X1),X2)),negate(add(negate(X1),negate(X2)))) = X1,
inference(orient,[status(thm)],[t532]) ).
cnf(f4,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_huntingtons_axiom) ).
fof(f4_nnf,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
add(negate(add(a,negate(b))),negate(add(negate(b),negate(a)))) != b,
inference(rw,[status(thm)],[goal_0,t13]) ).
cnf(g0_1,plain,
add(negate(add(negate(b),a)),negate(add(negate(b),negate(a)))) != b,
inference(rw,[status(thm)],[g0_0,t13]) ).
cnf(g0_2,plain,
b != b,
inference(rw,[status(thm)],[g0_1,t589]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB021-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.58 % Computer : n008.cluster.edu
% 0.09/5.58 % Model : x86_64 x86_64
% 0.09/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.58 % Memory : 8046.5625MB
% 0.09/5.58 % OS : Linux 6.8.0-71-generic
% 0.09/5.58 % CPULimit : 300
% 0.09/5.58 % WCLimit : 300
% 0.09/5.58 % DateTime : Thu Sep 24 08:29:03 UTC 2026
% 0.09/5.58 % CPUTime :
% 0.09/5.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.24/6.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.24/6.65 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------