%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG362-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Thu Sep 24 11:50:05 AM UTC 2026
% Result : Unsatisfiable 4.43s 1.09s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG362-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.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 : Mon Sep 21 13:12:58 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.15/0.45 % Drodi V4.1.1
% 4.43/1.09 % Refutation found
% 4.43/1.09 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.43/1.09 % SZS output start CNFRefutation for theBenchmark
% 4.43/1.09 fof(f398,axiom,(
% 4.43/1.09 (![T_a,V_a]: (( ~ class_OrderedGroup_Omonoid__add(T_a)| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ))),
% 4.43/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.43/1.09 fof(f472,axiom,(
% 4.43/1.09 (![T_a]: (( ~ class_Ring__and__Field_Oordered__semidom(T_a)| ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ))),
% 4.43/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.43/1.09 fof(f624,axiom,(
% 4.43/1.09 (![V_x]: (c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(V_x),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal) ))),
% 4.43/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.43/1.09 fof(f625,axiom,(
% 4.43/1.09 (![V_n]: (c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,V_n),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ))),
% 4.43/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.43/1.09 fof(f626,axiom,(
% 4.43/1.09 (![V_w,V_z]: (( c_lessequals(V_w,V_z,tc_RealDef_Oreal)| c_lessequals(V_z,V_w,tc_RealDef_Oreal) ) ))),
% 4.43/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.43/1.09 fof(f632,axiom,(
% 4.43/1.09 (![V_i,V_k,V_j]: (( c_lessequals(V_i,V_k,tc_RealDef_Oreal)| ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)| ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal) ) ))),
% 4.43/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.43/1.09 fof(f655,axiom,(
% 4.43/1.09 (![V_z,V_x,V_y]: (( c_lessequals(c_HOL_Oplus__class_Oplus(V_z,V_x,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)| ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ))),
% 4.43/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.43/1.09 fof(f659,axiom,(
% 4.43/1.09 (![V_z,V_w]: (( V_z = V_w| ~ c_lessequals(V_w,V_z,tc_RealDef_Oreal)| ~ c_lessequals(V_z,V_w,tc_RealDef_Oreal) ) ))),
% 4.43/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.43/1.09 fof(f675,negated_conjecture,(
% 4.43/1.09 ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
% 4.43/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.43/1.09 fof(f729,axiom,(
% 4.43/1.09 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ),
% 4.43/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.43/1.09 fof(f753,axiom,(
% 4.43/1.09 class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
% 4.43/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.43/1.09 fof(f1441,plain,(
% 4.43/1.09 ![T_a]: (~class_OrderedGroup_Omonoid__add(T_a)|(![V_a]: c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a))),
% 4.43/1.09 inference(miniscoping,[status(thm)],[f398])).
% 4.43/1.09 fof(f1442,plain,(
% 4.43/1.09 ![X0,X1]: (~class_OrderedGroup_Omonoid__add(X0)|c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0)=X1)),
% 4.43/1.09 inference(cnf_transformation,[status(thm)],[f1441])).
% 4.43/1.09 fof(f1558,plain,(
% 4.43/1.09 ![X0]: (~class_Ring__and__Field_Oordered__semidom(X0)|~c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0))),
% 4.43/1.09 inference(cnf_transformation,[status(thm)],[f472])).
% 4.43/1.09 fof(f1772,plain,(
% 4.43/1.09 ![X0]: (c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(X0),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal))),
% 4.43/1.09 inference(cnf_transformation,[status(thm)],[f624])).
% 4.43/1.09 fof(f1773,plain,(
% 4.43/1.09 ![X0]: (c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal))),
% 4.43/1.09 inference(cnf_transformation,[status(thm)],[f625])).
% 4.43/1.09 fof(f1774,plain,(
% 4.43/1.09 ![X0,X1]: (c_lessequals(X0,X1,tc_RealDef_Oreal)|c_lessequals(X1,X0,tc_RealDef_Oreal))),
% 4.43/1.09 inference(cnf_transformation,[status(thm)],[f626])).
% 4.43/1.09 fof(f1783,plain,(
% 4.43/1.09 ![V_i,V_j]: ((![V_k]: (c_lessequals(V_i,V_k,tc_RealDef_Oreal)|~c_lessequals(V_j,V_k,tc_RealDef_Oreal)))|~c_lessequals(V_i,V_j,tc_RealDef_Oreal))),
% 4.43/1.09 inference(miniscoping,[status(thm)],[f632])).
% 4.43/1.09 fof(f1784,plain,(
% 4.43/1.09 ![X0,X1,X2]: (c_lessequals(X0,X1,tc_RealDef_Oreal)|~c_lessequals(X2,X1,tc_RealDef_Oreal)|~c_lessequals(X0,X2,tc_RealDef_Oreal))),
% 4.43/1.09 inference(cnf_transformation,[status(thm)],[f1783])).
% 4.43/1.09 fof(f1828,plain,(
% 4.43/1.09 ![V_x,V_y]: ((![V_z]: c_lessequals(c_HOL_Oplus__class_Oplus(V_z,V_x,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal))|~c_lessequals(V_x,V_y,tc_RealDef_Oreal))),
% 4.43/1.09 inference(miniscoping,[status(thm)],[f655])).
% 4.43/1.09 fof(f1829,plain,(
% 4.43/1.09 ![X0,X1,X2]: (c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)|~c_lessequals(X1,X2,tc_RealDef_Oreal))),
% 4.43/1.09 inference(cnf_transformation,[status(thm)],[f1828])).
% 4.43/1.09 fof(f1833,plain,(
% 4.43/1.09 ![X0,X1]: (X0=X1|~c_lessequals(X1,X0,tc_RealDef_Oreal)|~c_lessequals(X0,X1,tc_RealDef_Oreal))),
% 4.43/1.09 inference(cnf_transformation,[status(thm)],[f659])).
% 4.43/1.09 fof(f1859,plain,(
% 4.43/1.09 ~c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
% 4.43/1.09 inference(cnf_transformation,[status(thm)],[f675])).
% 4.43/1.09 fof(f1913,plain,(
% 4.43/1.09 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal)),
% 4.43/1.09 inference(cnf_transformation,[status(thm)],[f729])).
% 4.43/1.09 fof(f1937,plain,(
% 4.43/1.09 class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal)),
% 4.43/1.09 inference(cnf_transformation,[status(thm)],[f753])).
% 4.43/1.09 fof(f1987,plain,(
% 4.43/1.09 c_lessequals(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),tc_RealDef_Oreal)),
% 4.43/1.09 inference(resolution,[status(thm)],[f1774,f1859])).
% 4.43/1.09 fof(f2005,plain,(
% 4.43/1.09 ![X0]: (c_RealVector_Onorm__class_Onorm(hAPP(v_s,X0),tc_Complex_Ocomplex)=v_r|~c_lessequals(v_r,c_RealVector_Onorm__class_Onorm(hAPP(v_s,X0),tc_Complex_Ocomplex),tc_RealDef_Oreal))),
% 4.43/1.09 inference(resolution,[status(thm)],[f1773,f1833])).
% 4.43/1.09 fof(f2163,plain,(
% 4.43/1.09 ![X0]: (c_lessequals(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)|~c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),X0,tc_RealDef_Oreal))),
% 4.43/1.09 inference(resolution,[status(thm)],[f1784,f1987])).
% 4.43/1.09 fof(f2274,plain,(
% 4.43/1.09 c_lessequals(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),tc_RealDef_Oreal)),
% 4.43/1.09 inference(resolution,[status(thm)],[f2163,f1772])).
% 4.43/1.09 fof(f2287,plain,(
% 4.43/1.09 ![X0]: (c_lessequals(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)|~c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal))),
% 4.43/1.09 inference(resolution,[status(thm)],[f2274,f1784])).
% 4.43/1.09 fof(f2288,plain,(
% 4.43/1.09 ![X0]: (c_lessequals(X0,c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),tc_RealDef_Oreal)|~c_lessequals(X0,c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))),
% 4.43/1.09 inference(resolution,[status(thm)],[f2274,f1784])).
% 4.43/1.09 fof(f2377,plain,(
% 4.43/1.09 c_lessequals(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)),
% 4.43/1.09 inference(resolution,[status(thm)],[f2287,f1773])).
% 4.43/1.09 fof(f2393,plain,(
% 4.43/1.09 c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)=v_r|~c_lessequals(v_r,c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
% 4.43/1.09 inference(resolution,[status(thm)],[f2377,f1833])).
% 4.43/1.09 fof(f4499,plain,(
% 4.43/1.09 ![X0]: (c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)=X0)),
% 4.43/1.09 inference(resolution,[status(thm)],[f1442,f1937])).
% 4.43/1.09 fof(f6405,plain,(
% 4.43/1.09 ~class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal)|c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)),
% 4.43/1.09 inference(resolution,[status(thm)],[f1558,f1774])).
% 4.43/1.09 fof(f6410,plain,(
% 4.43/1.09 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)),
% 4.43/1.09 inference(forward_subsumption_resolution,[status(thm)],[f6405,f1913])).
% 4.43/1.09 fof(f6497,plain,(
% 4.43/1.10 ![X0]: (c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))),
% 4.43/1.10 inference(resolution,[status(thm)],[f6410,f1829])).
% 4.43/1.10 fof(f6511,plain,(
% 4.43/1.10 ![X0]: (c_lessequals(X0,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))),
% 4.43/1.10 inference(forward_demodulation,[status(thm)],[f4499,f6497])).
% 4.43/1.10 fof(f6558,plain,(
% 4.43/1.10 c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)=v_r),
% 4.43/1.10 inference(backward_subsumption_resolution,[status(thm)],[f2393,f6511])).
% 4.43/1.10 fof(f6580,plain,(
% 4.43/1.10 c_lessequals(v_r,c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),tc_RealDef_Oreal)),
% 4.43/1.10 inference(resolution,[status(thm)],[f6511,f2288])).
% 4.43/1.10 fof(f6664,plain,(
% 4.43/1.10 ~c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)),
% 4.43/1.10 inference(backward_demodulation,[status(thm)],[f6558,f1859])).
% 4.43/1.10 fof(f6932,plain,(
% 4.43/1.10 c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex)=v_r),
% 4.43/1.10 inference(resolution,[status(thm)],[f6580,f2005])).
% 4.43/1.10 fof(f6971,plain,(
% 4.43/1.10 c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)),
% 4.43/1.10 inference(paramodulation,[status(thm)],[f6932,f1772])).
% 4.43/1.10 fof(f6981,plain,(
% 4.43/1.10 $false),
% 4.43/1.10 inference(forward_subsumption_resolution,[status(thm)],[f6971,f6664])).
% 4.43/1.10 % SZS output end CNFRefutation for theBenchmark.p
% 0.82/1.11 % Elapsed time: 0.742363 seconds
% 0.82/1.11 % CPU time: 4.993486 seconds
% 0.82/1.11 % Total memory used: 193.480 MB
% 0.82/1.11 % Net memory used: 189.753 MB
%------------------------------------------------------------------------------