%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET838-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 02:44:05 PM UTC 2026
% Result : Unsatisfiable 3.30s 0.84s
% Output : Proof 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 31 unt; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 24 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,negated_conjecture,
( v_g(v_f(V_U)) != V_U
| v_xa(V_U) != V_U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3_nnf,plain,
! [V_U] :
( v_g(v_f(V_U)) != V_U
| v_xa(V_U) != V_U ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_U] :
( v_g(v_f(V_U)) != V_U
| v_xa(V_U) != V_U ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( v_g(v_f(X0)) != X0
| v_xa(X0) != X0 ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t4,plain,
ifeq(v_xa(X1),X1,ifeq(v_g(v_f(X1)),X1,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t10,plain,
ifeq(v_xa(X1),X1,ifeq(v_g(v_f(X1)),X1,false,true),true) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(f2,negated_conjecture,
( v_g(v_f(V_U)) != V_U
| v_g(v_f(v_xa(V_U))) = v_xa(V_U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2_nnf,plain,
! [V_U] :
( v_g(v_f(V_U)) != V_U
| v_g(v_f(v_xa(V_U))) = v_xa(V_U) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_U] :
( v_g(v_f(V_U)) != V_U
| v_g(v_f(v_xa(V_U))) = v_xa(V_U) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( v_g(v_f(X0)) != X0
| v_g(v_f(v_xa(X0))) = v_xa(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t3,plain,
ifeq(v_g(v_f(X1)),X1,v_g(v_f(v_xa(X1))),v_xa(X1)) = v_xa(X1),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t7,plain,
ifeq(v_g(v_f(X1)),X1,v_g(v_f(v_xa(X1))),v_xa(X1)) = v_xa(X1),
inference(orient,[status(thm)],[t3]) ).
cnf(f1,negated_conjecture,
( v_f(v_g(V_U)) != V_U
| V_U = v_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
! [V_U] :
( v_f(v_g(V_U)) != V_U
| V_U = v_x ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_U] :
( v_f(v_g(V_U)) != V_U
| V_U = v_x ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( v_f(v_g(X0)) != X0
| X0 = v_x ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t2,plain,
ifeq(v_f(v_g(X1)),X1,X1,v_x) = v_x,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t9,plain,
ifeq(v_f(v_g(X1)),X1,X1,v_x) = v_x,
inference(orient,[status(thm)],[t2]) ).
cnf(f0,negated_conjecture,
v_f(v_g(v_x)) = v_x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
v_f(v_g(v_x)) = v_x,
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
v_f(v_g(v_x)) = v_x,
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(t0,plain,
v_f(v_g(v_x)) = v_x,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t6,plain,
v_f(v_g(v_x)) = v_x,
inference(orient,[status(thm)],[t0]) ).
cnf(t8,plain,
v_xa(v_g(v_x)) = ifeq(v_g(v_x),v_g(v_x),v_g(v_f(v_xa(v_g(v_x)))),v_xa(v_g(v_x))),
inference(cp,[status(thm)],[t7,t6]) ).
cnf(t1,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t25,plain,
v_xa(v_g(v_x)) = v_g(v_f(v_xa(v_g(v_x)))),
inference(step,[status(thm)],[t8,t5]) ).
cnf(t12,plain,
v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)),
inference(orient,[status(thm)],[t25]) ).
cnf(t13,plain,
v_x = ifeq(v_f(v_xa(v_g(v_x))),v_f(v_xa(v_g(v_x))),v_f(v_xa(v_g(v_x))),v_x),
inference(cp,[status(thm)],[t9,t12]) ).
cnf(t26,plain,
v_x = v_f(v_xa(v_g(v_x))),
inference(step,[status(thm)],[t13,t5]) ).
cnf(t16,plain,
v_f(v_xa(v_g(v_x))) = v_x,
inference(orient,[status(thm)],[t26]) ).
cnf(t18,plain,
v_xa(v_g(v_x)) = ifeq(v_g(v_f(v_g(v_x))),v_g(v_x),v_g(v_x),v_xa(v_g(v_x))),
inference(cp,[status(thm)],[t7,t16]) ).
cnf(t28,plain,
v_xa(v_g(v_x)) = ifeq(v_g(v_x),v_g(v_x),v_g(v_x),v_xa(v_g(v_x))),
inference(step,[status(thm)],[t18,t6]) ).
cnf(t29,plain,
v_xa(v_g(v_x)) = v_g(v_x),
inference(step,[status(thm)],[t28,t5]) ).
cnf(t21,plain,
v_xa(v_g(v_x)) = v_g(v_x),
inference(orient,[status(thm)],[t29]) ).
cnf(t22,plain,
true = ifeq(v_g(v_x),v_g(v_x),ifeq(v_g(v_f(v_g(v_x))),v_g(v_x),false,true),true),
inference(cp,[status(thm)],[t10,t21]) ).
cnf(t30,plain,
true = ifeq(v_g(v_f(v_g(v_x))),v_g(v_x),false,true),
inference(step,[status(thm)],[t22,t5]) ).
cnf(t31,plain,
true = ifeq(v_g(v_x),v_g(v_x),false,true),
inference(step,[status(thm)],[t30,t6]) ).
cnf(t32,plain,
true = false,
inference(step,[status(thm)],[t31,t5]) ).
cnf(t23,plain,
false = true,
inference(orient,[status(thm)],[t32]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t23]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET838-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n017.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 12:04:47 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.30/0.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.30/0.84 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------