%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LDA003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 02:10:49 PM UTC 2026
% Result : Unsatisfiable 6.75s 1.34s
% Output : Proof 6.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 42 unt; 0 def)
% Number of atoms : 42 ( 33 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 12 ( 12 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 32 ( 4 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
u = f(n2,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f5_nnf,plain,
u = f(n2,n2),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
u = f(n2,n2),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(t2,plain,
f(n2,n2) = u,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t21,plain,
f(n2,n2) = u,
inference(orient,[status(thm)],[t2]) ).
cnf(f4,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f4_nnf,plain,
n3 = f(n2,n1),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
n3 = f(n2,n1),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(t1,plain,
f(n2,n1) = n3,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t24,plain,
f(n2,n1) = n3,
inference(orient,[status(thm)],[t1]) ).
cnf(f3,axiom,
n2 = f(n1,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
fof(f3_nnf,plain,
n2 = f(n1,n1),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
n2 = f(n1,n1),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(t0,plain,
f(n1,n1) = n2,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t27,plain,
f(n1,n1) = n2,
inference(orient,[status(thm)],[t0]) ).
cnf(f0,axiom,
f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
fof(f0_nnf,plain,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
f(X0,f(X1,X2)) = f(f(X0,X1),f(X0,X2)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t7,plain,
f(f(X1,X2),f(X1,X3)) = f(X1,f(X2,X3)),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t18,plain,
f(f(X1,X2),f(X1,X3)) = f(X1,f(X2,X3)),
inference(orient,[status(thm)],[t7]) ).
cnf(t25,plain,
f(n2,f(n1,X1)) = f(n3,f(n2,X1)),
inference(cp,[status(thm)],[t18,t24]) ).
cnf(t246,plain,
f(n2,f(n1,X1)) = f(n3,f(n2,X1)),
inference(orient,[status(thm)],[t25]) ).
cnf(f1,axiom,
left(X,f(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(f1_nnf,plain,
! [X,Y] : left(X,f(X,Y)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] : left(X,f(X,Y)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
left(X0,f(X0,X1)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t4,plain,
left(X1,f(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t30,plain,
left(X1,f(X1,X2)) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(f6,negated_conjecture,
~ left(n3,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
fof(f6_nnf,plain,
~ left(n3,u),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
~ left(n3,u),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
~ left(n3,u),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(goal_0,negated_conjecture,
left(n3,u) != true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(g0_0,plain,
left(n3,f(n2,n2)) != true,
inference(rw,[status(thm)],[goal_0,t21]) ).
cnf(g0_1,plain,
left(f(n2,n1),f(n2,n2)) != true,
inference(rw,[status(thm)],[g0_0,t24]) ).
cnf(g0_2,plain,
left(f(n2,n1),f(n2,f(n1,n1))) != true,
inference(rw,[status(thm)],[g0_1,t27]) ).
cnf(g0_3,plain,
left(f(n2,n1),f(n3,f(n2,n1))) != true,
inference(rw,[status(thm)],[g0_2,t246]) ).
cnf(g0_4,plain,
left(f(n2,n1),f(n3,n3)) != true,
inference(rw,[status(thm)],[g0_3,t24]) ).
cnf(g0_5,plain,
left(n3,f(n3,n3)) != true,
inference(rw,[status(thm)],[g0_4,t24]) ).
cnf(g0_6,plain,
true != true,
inference(rw,[status(thm)],[g0_5,t30]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n003.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
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 00:46:49 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.75/1.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.75/1.34 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------