%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ROB011-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 : Fri Sep 25 02:39:35 PM UTC 2026
% Result : Unsatisfiable 6.82s 1.36s
% Output : Proof 6.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 57 unt; 0 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 23 ( 23 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,axiom,
multiply(one,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_times_x) ).
fof(f3_nnf,plain,
! [X] : multiply(one,X) = X,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : multiply(one,X) = X,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
multiply(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t1,plain,
multiply(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t19,plain,
multiply(one,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
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(t2,plain,
add(X1,X2) = add(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t21,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t2]) ).
cnf(f7,hypothesis,
negate(add(a,negate(b))) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
fof(f7_nnf,plain,
negate(add(a,negate(b))) = c,
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
negate(add(a,negate(b))) = c,
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(t4,plain,
negate(add(a,negate(b))) = c,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t47,plain,
negate(add(a,negate(b))) = c,
inference(orient,[status(thm)],[t4]) ).
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(t7,plain,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t15,plain,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t49,plain,
a = negate(add(negate(add(a,b)),c)),
inference(cp,[status(thm)],[t15,t47]) ).
cnf(t168,plain,
a = negate(add(c,negate(add(a,b)))),
inference(step,[status(thm)],[t49,t21]) ).
cnf(t169,plain,
a = negate(add(c,negate(add(b,a)))),
inference(step,[status(thm)],[t168,t21]) ).
cnf(t129,plain,
negate(add(c,negate(add(b,a)))) = a,
inference(orient,[status(thm)],[t169]) ).
cnf(f1,axiom,
add(add(X,Y),Z) = add(X,add(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).
fof(f1_nnf,plain,
! [X,Y,Z] : add(add(X,Y),Z) = add(X,add(Y,Z)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] : add(add(X,Y),Z) = add(X,add(Y,Z)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t6,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t24,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(orient,[status(thm)],[t6]) ).
cnf(f8,negated_conjecture,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_base_step) ).
fof(f8_nnf,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != c,
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != c,
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != c,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != c,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(a,negate(add(b,add(a,c))))),
inference(rw,[status(thm)],[goal_0,t19]) ).
cnf(g0_1,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(a,negate(add(b,add(c,a))))),
inference(rw,[status(thm)],[g0_0,t21]) ).
cnf(g0_2,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(a,negate(add(add(c,a),b)))),
inference(rw,[status(thm)],[g0_1,t21]) ).
cnf(g0_3,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(a,negate(add(add(negate(add(a,negate(b))),a),b)))),
inference(rw,[status(thm)],[g0_2,t47]) ).
cnf(g0_4,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(a,negate(add(add(negate(add(negate(b),a)),a),b)))),
inference(rw,[status(thm)],[g0_3,t21]) ).
cnf(g0_5,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(negate(add(c,negate(add(b,a)))),negate(add(add(negate(add(negate(b),a)),a),b)))),
inference(rw,[status(thm)],[g0_4,t129]) ).
cnf(g0_6,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(negate(add(c,negate(add(a,b)))),negate(add(add(negate(add(negate(b),a)),a),b)))),
inference(rw,[status(thm)],[g0_5,t21]) ).
cnf(g0_7,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(negate(add(c,negate(add(a,b)))),negate(add(add(negate(add(a,negate(b))),a),b)))),
inference(rw,[status(thm)],[g0_6,t21]) ).
cnf(g0_8,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(negate(add(c,negate(add(a,b)))),negate(add(add(a,negate(add(a,negate(b)))),b)))),
inference(rw,[status(thm)],[g0_7,t21]) ).
cnf(g0_9,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(negate(add(c,negate(add(a,b)))),negate(add(b,add(a,negate(add(a,negate(b)))))))),
inference(rw,[status(thm)],[g0_8,t21]) ).
cnf(g0_10,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(negate(add(negate(add(a,b)),c)),negate(add(b,add(a,negate(add(a,negate(b)))))))),
inference(rw,[status(thm)],[g0_9,t21]) ).
cnf(g0_11,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(negate(add(negate(add(a,b)),c)),negate(add(b,add(a,c))))),
inference(rw,[status(thm)],[g0_10,t47]) ).
cnf(g0_12,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(negate(add(negate(add(a,b)),c)),negate(add(add(a,c),b)))),
inference(rw,[status(thm)],[g0_11,t21]) ).
cnf(g0_13,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(negate(add(negate(add(a,b)),c)),negate(add(add(c,a),b)))),
inference(rw,[status(thm)],[g0_12,t21]) ).
cnf(g0_14,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(negate(add(add(c,a),b)),negate(add(negate(add(a,b)),c)))),
inference(rw,[status(thm)],[g0_13,t21]) ).
cnf(g0_15,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(negate(add(add(c,a),b)),negate(add(c,negate(add(a,b)))))),
inference(rw,[status(thm)],[g0_14,t21]) ).
cnf(g0_16,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(negate(add(c,add(a,b))),negate(add(c,negate(add(a,b)))))),
inference(rw,[status(thm)],[g0_15,t24]) ).
cnf(g0_17,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != c,
inference(rw,[status(thm)],[g0_16,t15]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ROB011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 08:26:13 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.82/1.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.82/1.36 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------