%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG341-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 12:52:20 PM UTC 2026
% Result : Unsatisfiable 21.30s 13.11s
% Output : Proof 21.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 32 unt; 0 def)
% Number of atoms : 56 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 34 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 33 ( 6 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f473,negated_conjecture,
~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f473_nnf,plain,
~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f473]) ).
fof(f473_sk,plain,
~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f473_nnf]) ).
cnf(c473,plain,
~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f473_sk]) ).
cnf(t86,plain,
ifeq(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c473]) ).
cnf(f464,axiom,
( ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal)
| ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
| c_lessequals(V_i,V_k,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f464_nnf,plain,
! [V_i,V_k,V_j] :
( ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal)
| ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
| c_lessequals(V_i,V_k,tc_RealDef_Oreal) ),
inference(nnf_transformation,[status(thm)],[f464]) ).
fof(f464_sk,plain,
! [V_i,V_k,V_j] :
( ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal)
| ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
| c_lessequals(V_i,V_k,tc_RealDef_Oreal) ),
inference(skolemisation,[status(esa)],[f464_nnf]) ).
cnf(c464,plain,
( ~ c_lessequals(X0,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(esa)],[f464_sk]) ).
cnf(hi461,axiom,
ifeq(c_lessequals(X0,X1,tc_RealDef_Oreal),true,ifeq(c_lessequals(X2,X0,tc_RealDef_Oreal),true,c_lessequals(X2,X1,tc_RealDef_Oreal),true),true) = true,
inference(equality_encoding,[status(esa)],[c464]) ).
cnf(f472,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f472_nnf,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f472]) ).
cnf(c472,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f472_nnf]) ).
cnf(hi469,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) = true,
inference(equality_encoding,[status(esa)],[c472]) ).
cnf(f471,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f471_nnf,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f471]) ).
cnf(c471,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f471_nnf]) ).
cnf(hi468,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal) = true,
inference(equality_encoding,[status(esa)],[c471]) ).
cnf(t17,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) = true,
inference(hyper_resolution,[status(thm)],[hi461,hi469,hi468]) ).
cnf(t870,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(t1156,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t86,t870]) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t214,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t18]) ).
cnf(t1157,plain,
false = true,
inference(step,[status(thm)],[t1156,t214]) ).
cnf(t1117,plain,
false = true,
inference(orient,[status(thm)],[t1157]) ).
cnf(f173,axiom,
( c_Transcendental_Oexp(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a)
| ~ class_SEQ_Obanach(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp__not__eq__zero_0) ).
fof(f173_nnf,plain,
! [T_a,V_x] :
( c_Transcendental_Oexp(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a)
| ~ class_SEQ_Obanach(T_a) ),
inference(nnf_transformation,[status(thm)],[f173]) ).
fof(f173_sk,plain,
! [T_a,V_x] :
( c_Transcendental_Oexp(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a)
| ~ class_SEQ_Obanach(T_a) ),
inference(skolemisation,[status(esa)],[f173_nnf]) ).
cnf(c173,plain,
( c_Transcendental_Oexp(X1,X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| ~ class_SEQ_Obanach(X0) ),
inference(cnf_transformation,[status(esa)],[f173_sk]) ).
cnf(f219,axiom,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__neq__zero_0) ).
fof(f219_nnf,plain,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f219]) ).
fof(f219_sk,plain,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f219_nnf]) ).
cnf(c219,plain,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f219_sk]) ).
cnf(f447,axiom,
~ c_lessequals(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__exp__le__zero_0) ).
fof(f447_nnf,plain,
! [V_x] : ~ c_lessequals(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(nnf_transformation,[status(thm)],[f447]) ).
fof(f447_sk,plain,
! [V_x] : ~ c_lessequals(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(skolemisation,[status(esa)],[f447_nnf]) ).
cnf(c447,plain,
~ c_lessequals(c_Transcendental_Oexp(X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(esa)],[f447_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c173,c219,c447,c473]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1117]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG341-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/10.37 % Computer : n006.cluster.edu
% 0.11/10.37 % Model : x86_64 x86_64
% 0.11/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.37 % Memory : 8046.5625MB
% 0.11/10.37 % OS : Linux 6.8.0-71-generic
% 0.11/10.37 % CPULimit : 300
% 0.11/10.37 % WCLimit : 300
% 0.11/10.37 % DateTime : Fri Sep 25 05:25:54 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 21.30/13.11 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.30/13.11 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------