%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LDA007-2 : TPTP v9.3.1. Bugfixed v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 5.32s 1.27s
% Output : Proof 5.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 103 ( 95 unt; 0 def)
% Number of atoms : 111 ( 94 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 29 ( 21 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-4 aty)
% Number of variables : 72 ( 2 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f19,negated_conjecture,
f(t,tsk) != f(tt_ts,tk),
file('/export/starexec/sandbox/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(t75,plain,
ifeq(f(t,tsk),f(tt_ts,tk),false,true) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(f7,axiom,
( less(X,a(U,X))
| less(X,critical_point(U)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c3) ).
fof(f7_nnf,plain,
! [X,U] :
( less(X,a(U,X))
| less(X,critical_point(U)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,U] :
( less(X,a(U,X))
| less(X,critical_point(U)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( less(X0,a(X1,X0))
| less(X0,critical_point(X1)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t23,plain,
or(less(X1,critical_point(X2)),less(X1,a(X2,X1))) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t80,plain,
or(less(X1,critical_point(X2)),less(X1,a(X2,X1))) = true,
inference(orient,[status(thm)],[t23]) ).
cnf(f2,axiom,
critical_point(f(U,V)) = a(U,critical_point(V)),
file('/export/starexec/sandbox/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(t103,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/sandbox/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(t39,plain,
f(t,t) = tt,
inference(orient,[status(thm)],[t7]) ).
cnf(t111,plain,
a(t,critical_point(t)) = critical_point(tt),
inference(cp,[status(thm)],[t103,t39]) ).
cnf(f13,axiom,
k = critical_point(t),
file('/export/starexec/sandbox/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(t121,plain,
critical_point(t) = k,
inference(orient,[status(thm)],[t0]) ).
cnf(t423,plain,
a(t,k) = critical_point(tt),
inference(step,[status(thm)],[t111,t121]) ).
cnf(t189,plain,
a(t,k) = critical_point(tt),
inference(orient,[status(thm)],[t423]) ).
cnf(t194,plain,
true = or(less(k,critical_point(t)),less(k,critical_point(tt))),
inference(cp,[status(thm)],[t80,t189]) ).
cnf(t424,plain,
true = or(less(k,k),less(k,critical_point(tt))),
inference(step,[status(thm)],[t194,t121]) ).
cnf(f3,axiom,
~ less(X,X),
file('/export/starexec/sandbox/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(t115,plain,
less(X1,X1) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t425,plain,
true = or(false,less(k,critical_point(tt))),
inference(step,[status(thm)],[t424,t115]) ).
cnf(t14,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t34,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t14]) ).
cnf(t426,plain,
true = less(k,critical_point(tt)),
inference(step,[status(thm)],[t425,t34]) ).
cnf(t198,plain,
less(k,critical_point(tt)) = true,
inference(orient,[status(thm)],[t426]) ).
cnf(f6,axiom,
( a(U,X) = X
| ~ less(X,critical_point(U)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2) ).
fof(f6_nnf,plain,
! [X,U] :
( a(U,X) = X
| ~ less(X,critical_point(U)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,U] :
( a(U,X) = X
| ~ less(X,critical_point(U)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( a(X1,X0) = X0
| ~ less(X0,critical_point(X1)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t22,plain,
ifeq(less(X1,critical_point(X2)),true,a(X2,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t31,plain,
ifeq(less(X1,critical_point(X2)),true,a(X2,X1),X1) = X1,
inference(orient,[status(thm)],[t22]) ).
cnf(t200,plain,
k = ifeq(true,true,a(tt,k),k),
inference(cp,[status(thm)],[t31,t198]) ).
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(t427,plain,
k = a(tt,k),
inference(step,[status(thm)],[t200,t29]) ).
cnf(t201,plain,
a(tt,k) = k,
inference(orient,[status(thm)],[t427]) ).
cnf(t197,plain,
k = ifeq(less(k,critical_point(t)),true,critical_point(tt),k),
inference(cp,[status(thm)],[t31,t189]) ).
cnf(t430,plain,
k = ifeq(less(k,k),true,critical_point(tt),k),
inference(step,[status(thm)],[t197,t121]) ).
cnf(t431,plain,
k = ifeq(false,true,critical_point(tt),k),
inference(step,[status(thm)],[t430,t115]) ).
cnf(t223,plain,
ifeq(false,true,critical_point(tt),k) = k,
inference(orient,[status(thm)],[t431]) ).
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(t25,plain,
f(f(X1,X2),f(X1,X3)) = f(X1,f(X2,X3)),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t35,plain,
f(f(X1,X2),f(X1,X3)) = f(X1,f(X2,X3)),
inference(orient,[status(thm)],[t25]) ).
cnf(t40,plain,
f(t,f(t,X1)) = f(tt,f(t,X1)),
inference(cp,[status(thm)],[t35,t39]) ).
cnf(t226,plain,
f(t,f(t,X1)) = f(tt,f(t,X1)),
inference(orient,[status(thm)],[t40]) ).
cnf(f11,axiom,
ts = f(t,s),
file('/export/starexec/sandbox/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(t47,plain,
f(t,s) = ts,
inference(orient,[status(thm)],[t6]) ).
cnf(t227,plain,
f(tt,f(t,s)) = f(t,ts),
inference(cp,[status(thm)],[t226,t47]) ).
cnf(t435,plain,
f(tt,ts) = f(t,ts),
inference(step,[status(thm)],[t227,t47]) ).
cnf(f12,axiom,
tt_ts = f(tt,ts),
file('/export/starexec/sandbox/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(t55,plain,
f(tt,ts) = tt_ts,
inference(orient,[status(thm)],[t10]) ).
cnf(t436,plain,
tt_ts = f(t,ts),
inference(step,[status(thm)],[t435,t55]) ).
cnf(t235,plain,
f(t,ts) = tt_ts,
inference(orient,[status(thm)],[t436]) ).
cnf(f15,axiom,
tk = f(t,k),
file('/export/starexec/sandbox/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(t43,plain,
f(t,k) = tk,
inference(orient,[status(thm)],[t5]) ).
cnf(t45,plain,
f(t,f(X1,k)) = f(f(t,X1),tk),
inference(cp,[status(thm)],[t35,t43]) ).
cnf(t404,plain,
f(f(t,X1),tk) = f(t,f(X1,k)),
inference(orient,[status(thm)],[t45]) ).
cnf(f17,axiom,
tsk = f(ts,k),
file('/export/starexec/sandbox/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(t59,plain,
f(ts,k) = tsk,
inference(orient,[status(thm)],[t8]) ).
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,t75]) ).
cnf(g0_1,plain,
true != ifeq(f(t,tsk),f(tt_ts,tk),false,less(k,critical_point(tt))),
inference(rw,[status(thm)],[g0_0,t198]) ).
cnf(g0_2,plain,
true != ifeq(f(t,tsk),f(tt_ts,tk),false,less(a(tt,k),critical_point(tt))),
inference(rw,[status(thm)],[g0_1,t201]) ).
cnf(g0_3,plain,
true != ifeq(f(t,tsk),f(tt_ts,tk),false,less(a(tt,ifeq(false,true,critical_point(tt),k)),critical_point(tt))),
inference(rw,[status(thm)],[g0_2,t223]) ).
cnf(g0_4,plain,
true != ifeq(f(t,tsk),f(f(t,ts),tk),false,less(a(tt,ifeq(false,true,critical_point(tt),k)),critical_point(tt))),
inference(rw,[status(thm)],[g0_3,t235]) ).
cnf(g0_5,plain,
true != ifeq(f(t,tsk),f(t,f(ts,k)),false,less(a(tt,ifeq(false,true,critical_point(tt),k)),critical_point(tt))),
inference(rw,[status(thm)],[g0_4,t404]) ).
cnf(g0_6,plain,
true != ifeq(f(t,tsk),f(t,tsk),false,less(a(tt,ifeq(false,true,critical_point(tt),k)),critical_point(tt))),
inference(rw,[status(thm)],[g0_5,t59]) ).
cnf(g0_7,plain,
true != false,
inference(rw,[status(thm)],[g0_6,t29]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LDA007-2 : TPTP v9.3.1. Bugfixed v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 00:43:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.32/1.27 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.32/1.27 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------