%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LDA007-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 02:10:50 PM UTC 2026
% Result : Unsatisfiable 8.76s 1.62s
% Output : Proof 8.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 96 ( 88 unt; 0 def)
% Number of atoms : 104 ( 87 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 35 ( 27 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-4 aty)
% Number of variables : 76 ( 2 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f19,negated_conjecture,
f(t,tsk) != f(tt_ts,tk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
fof(f19_nnf,plain,
f(t,tsk) != f(tt_ts,tk),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
f(t,tsk) != f(tt_ts,tk),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
f(t,tsk) != f(tt_ts,tk),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t21,plain,
ifeq(f(t,tsk),f(tt_ts,tk),false,true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t34,plain,
ifeq(f(t,tsk),f(tt_ts,tk),false,true) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(f15,axiom,
tk = f(t,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
fof(f15_nnf,plain,
tk = f(t,k),
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c15,plain,
tk = f(t,k),
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(t5,plain,
f(t,k) = tk,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t49,plain,
f(t,k) = tk,
inference(orient,[status(thm)],[t5]) ).
cnf(f6,axiom,
( less(a(U,X),a(U,Y))
| ~ less(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b4) ).
fof(f6_nnf,plain,
! [X,Y,U] :
( less(a(U,X),a(U,Y))
| ~ less(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,U] :
( less(a(U,X),a(U,Y))
| ~ less(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( less(a(X2,X0),a(X2,X1))
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t27,plain,
ifeq(less(X1,X2),true,less(a(X3,X1),a(X3,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t35,plain,
ifeq(less(X1,X2),true,less(a(X3,X1),a(X3,X2)),true) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(f3,axiom,
~ less(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).
fof(f3_nnf,plain,
! [X] : ~ less(X,X),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : ~ less(X,X),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ less(X0,X0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t11,plain,
less(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t73,plain,
less(X1,X1) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t79,plain,
true = ifeq(false,true,less(a(X1,X2),a(X1,X2)),true),
inference(cp,[status(thm)],[t35,t73]) ).
cnf(t204,plain,
true = ifeq(false,true,false,true),
inference(step,[status(thm)],[t79,t73]) ).
cnf(t180,plain,
ifeq(false,true,false,true) = true,
inference(orient,[status(thm)],[t204]) ).
cnf(f7,axiom,
( a(U,X) = X
| ~ less(X,critical_point(U)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2) ).
fof(f7_nnf,plain,
! [X,U] :
( a(U,X) = X
| ~ less(X,critical_point(U)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,U] :
( a(U,X) = X
| ~ less(X,critical_point(U)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( a(X1,X0) = X0
| ~ less(X0,critical_point(X1)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t22,plain,
ifeq(less(X1,critical_point(X2)),true,a(X2,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t30,plain,
ifeq(less(X1,critical_point(X2)),true,a(X2,X1),X1) = X1,
inference(orient,[status(thm)],[t22]) ).
cnf(f2,axiom,
critical_point(f(U,V)) = a(U,critical_point(V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
fof(f2_nnf,plain,
! [U,V] : critical_point(f(U,V)) = a(U,critical_point(V)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [U,V] : critical_point(f(U,V)) = a(U,critical_point(V)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
critical_point(f(X0,X1)) = a(X0,critical_point(X1)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t17,plain,
critical_point(f(X1,X2)) = a(X1,critical_point(X2)),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t98,plain,
critical_point(f(X1,X2)) = a(X1,critical_point(X2)),
inference(orient,[status(thm)],[t17]) ).
cnf(f9,axiom,
tt = f(t,t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f9_nnf,plain,
tt = f(t,t),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
tt = f(t,t),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(t7,plain,
f(t,t) = tt,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t46,plain,
f(t,t) = tt,
inference(orient,[status(thm)],[t7]) ).
cnf(t106,plain,
a(t,critical_point(t)) = critical_point(tt),
inference(cp,[status(thm)],[t98,t46]) ).
cnf(f13,axiom,
k = critical_point(t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
fof(f13_nnf,plain,
k = critical_point(t),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
k = critical_point(t),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(t0,plain,
critical_point(t) = k,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t110,plain,
critical_point(t) = k,
inference(orient,[status(thm)],[t0]) ).
cnf(t199,plain,
a(t,k) = critical_point(tt),
inference(step,[status(thm)],[t106,t110]) ).
cnf(t158,plain,
a(t,k) = critical_point(tt),
inference(orient,[status(thm)],[t199]) ).
cnf(t160,plain,
k = ifeq(less(k,critical_point(t)),true,critical_point(tt),k),
inference(cp,[status(thm)],[t30,t158]) ).
cnf(t205,plain,
k = ifeq(less(k,k),true,critical_point(tt),k),
inference(step,[status(thm)],[t160,t110]) ).
cnf(t206,plain,
k = ifeq(false,true,critical_point(tt),k),
inference(step,[status(thm)],[t205,t73]) ).
cnf(t181,plain,
ifeq(false,true,critical_point(tt),k) = k,
inference(orient,[status(thm)],[t206]) ).
cnf(f0,axiom,
f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)),
file('/export/starexec/sandbox2/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(t25,plain,
f(f(X1,X2),f(X1,X3)) = f(X1,f(X2,X3)),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t43,plain,
f(f(X1,X2),f(X1,X3)) = f(X1,f(X2,X3)),
inference(orient,[status(thm)],[t25]) ).
cnf(t47,plain,
f(t,f(t,X1)) = f(tt,f(t,X1)),
inference(cp,[status(thm)],[t43,t46]) ).
cnf(t182,plain,
f(t,f(t,X1)) = f(tt,f(t,X1)),
inference(orient,[status(thm)],[t47]) ).
cnf(f11,axiom,
ts = f(t,s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f11_nnf,plain,
ts = f(t,s),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
ts = f(t,s),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(t6,plain,
f(t,s) = ts,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t52,plain,
f(t,s) = ts,
inference(orient,[status(thm)],[t6]) ).
cnf(t183,plain,
f(tt,f(t,s)) = f(t,ts),
inference(cp,[status(thm)],[t182,t52]) ).
cnf(t207,plain,
f(tt,ts) = f(t,ts),
inference(step,[status(thm)],[t183,t52]) ).
cnf(f12,axiom,
tt_ts = f(tt,ts),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
fof(f12_nnf,plain,
tt_ts = f(tt,ts),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
tt_ts = f(tt,ts),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(t10,plain,
f(tt,ts) = tt_ts,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t58,plain,
f(tt,ts) = tt_ts,
inference(orient,[status(thm)],[t10]) ).
cnf(t208,plain,
tt_ts = f(t,ts),
inference(step,[status(thm)],[t207,t58]) ).
cnf(t191,plain,
f(t,ts) = tt_ts,
inference(orient,[status(thm)],[t208]) ).
cnf(f17,axiom,
tsk = f(ts,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
fof(f17_nnf,plain,
tsk = f(ts,k),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
tsk = f(ts,k),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(t8,plain,
f(ts,k) = tsk,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t61,plain,
f(ts,k) = tsk,
inference(orient,[status(thm)],[t8]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t29,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c19]) ).
cnf(g0_0,plain,
true != ifeq(f(t,tsk),f(tt_ts,tk),false,true),
inference(rw,[status(thm)],[goal_0,t34]) ).
cnf(g0_1,plain,
true != ifeq(f(t,tsk),f(tt_ts,f(t,k)),false,true),
inference(rw,[status(thm)],[g0_0,t49]) ).
cnf(g0_2,plain,
true != ifeq(f(t,tsk),f(tt_ts,f(t,k)),false,ifeq(false,true,false,true)),
inference(rw,[status(thm)],[g0_1,t180]) ).
cnf(g0_3,plain,
true != ifeq(f(t,tsk),f(tt_ts,f(t,ifeq(false,true,critical_point(tt),k))),false,ifeq(false,true,false,true)),
inference(rw,[status(thm)],[g0_2,t181]) ).
cnf(g0_4,plain,
true != ifeq(f(t,tsk),f(f(t,ts),f(t,ifeq(false,true,critical_point(tt),k))),false,ifeq(false,true,false,true)),
inference(rw,[status(thm)],[g0_3,t191]) ).
cnf(g0_5,plain,
true != ifeq(f(t,tsk),f(t,f(ts,ifeq(false,true,critical_point(tt),k))),false,ifeq(false,true,false,true)),
inference(rw,[status(thm)],[g0_4,t43]) ).
cnf(g0_6,plain,
true != ifeq(f(t,tsk),f(t,f(ts,ifeq(false,true,critical_point(tt),k))),false,true),
inference(rw,[status(thm)],[g0_5,t180]) ).
cnf(g0_7,plain,
true != ifeq(f(t,tsk),f(t,f(ts,k)),false,true),
inference(rw,[status(thm)],[g0_6,t181]) ).
cnf(g0_8,plain,
true != ifeq(f(t,tsk),f(t,tsk),false,true),
inference(rw,[status(thm)],[g0_7,t61]) ).
cnf(g0_9,plain,
true != false,
inference(rw,[status(thm)],[g0_8,t29]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA007-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 00:45:18 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.76/1.62 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.76/1.62 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------