%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWX204+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 03:32:06 PM UTC 2026
% Result : Theorem 5.29s 1.13s
% Output : Proof 5.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 69 ( 69 unt; 0 def)
% Number of atoms : 69 ( 68 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 6 sgn 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : z != s(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
fof(f1_nnf,plain,
! [X] : z != s(X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : z != s(X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
z != s(X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t5,plain,
eq(z,s(X1)) = efalse,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t21,plain,
eq(z,s(X1)) = efalse,
inference(orient,[status(thm)],[t5]) ).
fof(f0,axiom,
! [X] : proj1S(s(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
fof(f0_nnf,plain,
! [X] : proj1S(s(X)) = X,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : proj1S(s(X)) = X,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
proj1S(s(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
proj1S(s(X1)) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t10,plain,
proj1S(s(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
fof(f5,axiom,
! [Y,N] : x22(s(N),Y) = x2(Y,x22(N,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
fof(f5_nnf,plain,
! [Y,N] : x22(s(N),Y) = x2(Y,x22(N,Y)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [N,Y] : x22(s(N),Y) = x2(Y,x22(N,Y)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
x22(s(X1),X0) = x2(X0,x22(X1,X0)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t7,plain,
x2(X1,x22(X2,X1)) = x22(s(X2),X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t15,plain,
x2(X1,x22(X2,X1)) = x22(s(X2),X1),
inference(orient,[status(thm)],[t7]) ).
fof(f4,axiom,
! [Y] : x22(z,Y) = z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
fof(f4_nnf,plain,
! [Y] : x22(z,Y) = z,
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [Y] : x22(z,Y) = z,
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
x22(z,X0) = z,
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t4,plain,
x22(z,X1) = z,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t14,plain,
x22(z,X1) = z,
inference(orient,[status(thm)],[t4]) ).
cnf(t18,plain,
x22(s(z),X1) = x2(X1,z),
inference(cp,[status(thm)],[t15,t14]) ).
cnf(t31,plain,
x22(s(z),X1) = x2(X1,z),
inference(orient,[status(thm)],[t18]) ).
cnf(t32,plain,
x22(s(s(z)),X1) = x2(X1,x2(X1,z)),
inference(cp,[status(thm)],[t15,t31]) ).
cnf(t58,plain,
x2(X1,x2(X1,z)) = x22(s(s(z)),X1),
inference(orient,[status(thm)],[t32]) ).
fof(f3,axiom,
! [Y,N] : x2(s(N),Y) = s(x2(N,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
fof(f3_nnf,plain,
! [Y,N] : x2(s(N),Y) = s(x2(N,Y)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [N,Y] : x2(s(N),Y) = s(x2(N,Y)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
x2(s(X1),X0) = s(x2(X1,X0)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t6,plain,
x2(s(X1),X2) = s(x2(X1,X2)),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t11,plain,
s(x2(X1,X2)) = x2(s(X1),X2),
inference(orient,[status(thm)],[t6]) ).
fof(f2,axiom,
! [Y] : x2(z,Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
fof(f2_nnf,plain,
! [Y] : x2(z,Y) = Y,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [Y] : x2(z,Y) = Y,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
x2(z,X0) = X0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t2,plain,
x2(z,X1) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t8,plain,
x2(z,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t12,plain,
x2(s(z),X1) = s(X1),
inference(cp,[status(thm)],[t11,t8]) ).
cnf(t23,plain,
x2(s(z),X1) = s(X1),
inference(orient,[status(thm)],[t12]) ).
cnf(t25,plain,
x2(s(s(z)),X1) = s(s(X1)),
inference(cp,[status(thm)],[t11,t23]) ).
cnf(t36,plain,
x2(s(s(z)),X1) = s(s(X1)),
inference(orient,[status(thm)],[t25]) ).
cnf(t60,plain,
x22(s(s(z)),s(s(z))) = x2(s(s(z)),s(s(z))),
inference(cp,[status(thm)],[t58,t36]) ).
fof(f6,conjecture,
? [X] : x22(X,X) != X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_007) ).
fof(f6_neg,negated_conjecture,
~ ? [X] : x22(X,X) != X,
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
! [X] : x22(X,X) = X,
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
! [X] : x22(X,X) = X,
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
x22(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t3,plain,
x22(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t9,plain,
x22(X1,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t84,plain,
s(s(z)) = x2(s(s(z)),s(s(z))),
inference(step,[status(thm)],[t60,t9]) ).
cnf(t85,plain,
s(s(z)) = s(s(s(s(z)))),
inference(step,[status(thm)],[t84,t36]) ).
cnf(t64,plain,
s(s(s(s(z)))) = s(s(z)),
inference(orient,[status(thm)],[t85]) ).
cnf(t65,plain,
s(s(s(z))) = proj1S(s(s(z))),
inference(cp,[status(thm)],[t10,t64]) ).
cnf(t86,plain,
s(s(s(z))) = s(z),
inference(step,[status(thm)],[t65,t10]) ).
cnf(t68,plain,
s(s(s(z))) = s(z),
inference(orient,[status(thm)],[t86]) ).
cnf(t69,plain,
s(s(z)) = proj1S(s(z)),
inference(cp,[status(thm)],[t10,t68]) ).
cnf(t87,plain,
s(s(z)) = z,
inference(step,[status(thm)],[t69,t10]) ).
cnf(t71,plain,
s(s(z)) = z,
inference(orient,[status(thm)],[t87]) ).
cnf(t75,plain,
efalse = eq(z,z),
inference(cp,[status(thm)],[t21,t71]) ).
cnf(t0,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t20,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t0]) ).
cnf(t94,plain,
efalse = etrue,
inference(step,[status(thm)],[t75,t20]) ).
cnf(t79,plain,
efalse = etrue,
inference(orient,[status(thm)],[t94]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t79]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX204+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n019.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
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 23:37:34 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.29/1.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.29/1.13 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------