%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP048-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 12:35:33 PM UTC 2026
% Result : Unsatisfiable 4.92s 1.22s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP048-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 19:56:32 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 4.92/1.22 % Refutation found
% 4.92/1.22 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.92/1.22 % SZS output start CNFRefutation for theBenchmark
% 4.92/1.22 fof(f1,axiom,(
% 4.92/1.22 (![A,B,C]: (ifeq(A,A,B,C) = B ))),
% 4.92/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.92/1.22 fof(f2,axiom,(
% 4.92/1.22 (![X]: (product(identity,X,X) = true ))),
% 4.92/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.92/1.22 fof(f3,axiom,(
% 4.92/1.22 (![X]: (product(inverse(X),X,identity) = true ))),
% 4.92/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.92/1.22 fof(f4,axiom,(
% 4.92/1.22 (![X,Y]: (product(X,Y,multiply(X,Y)) = true ))),
% 4.92/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.92/1.22 fof(f5,axiom,(
% 4.92/1.22 (![X,Y,W,Z]: (ifeq(product(X,Y,W),true,ifeq(product(X,Y,Z),true,equalish(Z,W),true),true) = true ))),
% 4.92/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.92/1.22 fof(f6,axiom,(
% 4.92/1.22 (![U,Z,W,Y,V,X]: (ifeq(product(U,Z,W),true,ifeq(product(Y,Z,V),true,ifeq(product(X,Y,U),true,product(X,V,W),true),true),true) = true ))),
% 4.92/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.92/1.22 fof(f8,axiom,(
% 4.92/1.22 (![X,Y,W,Z]: (ifeq(equalish(X,Y),true,ifeq(product(W,Z,X),true,product(W,Z,Y),true),true) = true ))),
% 4.92/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.92/1.22 fof(f9,hypothesis,(
% 4.92/1.22 equalish(a,b) = true ),
% 4.92/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.92/1.22 fof(f10,negated_conjecture,(
% 4.92/1.22 equalish(inverse(a),inverse(b)) != true ),
% 4.92/1.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.92/1.22 fof(f11,plain,(
% 4.92/1.22 ![X0,X1,X2]: (ifeq(X0,X0,X1,X2)=X1)),
% 4.92/1.22 inference(cnf_transformation,[status(thm)],[f1])).
% 4.92/1.22 fof(f12,plain,(
% 4.92/1.22 ![X0]: (product(identity,X0,X0)=true)),
% 4.92/1.22 inference(cnf_transformation,[status(thm)],[f2])).
% 4.92/1.22 fof(f13,plain,(
% 4.92/1.22 ![X0]: (product(inverse(X0),X0,identity)=true)),
% 4.92/1.22 inference(cnf_transformation,[status(thm)],[f3])).
% 4.92/1.22 fof(f14,plain,(
% 4.92/1.22 ![X0,X1]: (product(X0,X1,multiply(X0,X1))=true)),
% 4.92/1.22 inference(cnf_transformation,[status(thm)],[f4])).
% 4.92/1.22 fof(f15,plain,(
% 4.92/1.22 ![X0,X1,X2,X3]: (ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,equalish(X3,X2),true),true)=true)),
% 4.92/1.22 inference(cnf_transformation,[status(thm)],[f5])).
% 4.92/1.22 fof(f16,plain,(
% 4.92/1.22 ![X0,X1,X2,X3,X4,X5]: (ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X3,X0),true,product(X5,X4,X2),true),true),true)=true)),
% 4.92/1.22 inference(cnf_transformation,[status(thm)],[f6])).
% 4.92/1.22 fof(f18,plain,(
% 4.92/1.22 ![X0,X1,X2,X3]: (ifeq(equalish(X0,X1),true,ifeq(product(X2,X3,X0),true,product(X2,X3,X1),true),true)=true)),
% 4.92/1.22 inference(cnf_transformation,[status(thm)],[f8])).
% 4.92/1.22 fof(f19,plain,(
% 4.92/1.22 equalish(a,b)=true),
% 4.92/1.22 inference(cnf_transformation,[status(thm)],[f9])).
% 4.92/1.22 fof(f20,plain,(
% 4.92/1.22 ~equalish(inverse(a),inverse(b))=true),
% 4.92/1.22 inference(cnf_transformation,[status(thm)],[f10])).
% 4.92/1.22 fof(f21,definition,(
% 4.92/1.22 sF1_fnc=inverse(a)),
% 4.92/1.22 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 4.92/1.22 fof(f22,definition,(
% 4.92/1.22 sF2_fnc=inverse(b)),
% 4.92/1.22 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 4.92/1.22 fof(f23,definition,(
% 4.92/1.22 sF0_fnc=equalish(sF1_fnc,sF2_fnc)),
% 4.92/1.22 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 4.92/1.22 fof(f24,plain,(
% 4.92/1.22 ~sF0_fnc=true),
% 4.92/1.22 inference(definition_folding,[],[f20,f23,f22,f21])).
% 4.92/1.22 fof(f25,plain,(
% 4.92/1.22 product(sF2_fnc,b,identity)=true),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f22,f13])).
% 4.92/1.22 fof(f26,plain,(
% 4.92/1.22 product(sF1_fnc,a,identity)=true),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f21,f13])).
% 4.92/1.22 fof(f27,plain,(
% 4.92/1.22 ![X0,X1]: (ifeq(true,true,ifeq(product(inverse(X0),X0,X1),true,equalish(X1,identity),true),true)=true)),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f13,f15])).
% 4.92/1.22 fof(f33,plain,(
% 4.92/1.22 ![X0,X1]: (ifeq(product(X0,X1,sF2_fnc),true,ifeq(product(X0,X1,sF1_fnc),true,sF0_fnc,true),true)=true)),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f23,f15])).
% 4.92/1.22 fof(f35,plain,(
% 4.92/1.22 ![X0,X1]: (ifeq(product(inverse(X0),X0,X1),true,equalish(X1,identity),true)=true)),
% 4.92/1.22 inference(forward_demodulation,[status(thm)],[f11,f27])).
% 4.92/1.22 fof(f47,plain,(
% 4.92/1.22 ![X0,X1,X2,X3]: (ifeq(true,true,ifeq(product(X0,X1,X2),true,ifeq(product(X3,X0,identity),true,product(X3,X2,X1),true),true),true)=true)),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f12,f16])).
% 4.92/1.22 fof(f48,plain,(
% 4.92/1.22 ![X0,X1,X2,X3,X4]: (ifeq(true,true,ifeq(product(X0,X1,X2),true,ifeq(product(X3,X0,X4),true,product(X3,X2,multiply(X4,X1)),true),true),true)=true)),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f14,f16])).
% 4.92/1.22 fof(f63,plain,(
% 4.92/1.22 ![X0,X1,X2,X3]: (ifeq(product(X0,X1,X2),true,ifeq(product(X3,X0,identity),true,product(X3,X2,X1),true),true)=true)),
% 4.92/1.22 inference(forward_demodulation,[status(thm)],[f11,f47])).
% 4.92/1.22 fof(f64,plain,(
% 4.92/1.22 ![X0,X1,X2,X3,X4]: (ifeq(product(X0,X1,X2),true,ifeq(product(X3,X0,X4),true,product(X3,X2,multiply(X4,X1)),true),true)=true)),
% 4.92/1.22 inference(forward_demodulation,[status(thm)],[f11,f48])).
% 4.92/1.22 fof(f130,plain,(
% 4.92/1.22 ![X0,X1]: (ifeq(true,true,ifeq(product(X0,X1,a),true,product(X0,X1,b),true),true)=true)),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f19,f18])).
% 4.92/1.22 fof(f135,plain,(
% 4.92/1.22 ![X0,X1,X2]: (ifeq(equalish(multiply(X0,X1),X2),true,ifeq(true,true,product(X0,X1,X2),true),true)=true)),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f14,f18])).
% 4.92/1.22 fof(f141,plain,(
% 4.92/1.22 ![X0,X1]: (ifeq(product(X0,X1,a),true,product(X0,X1,b),true)=true)),
% 4.92/1.22 inference(forward_demodulation,[status(thm)],[f11,f130])).
% 4.92/1.22 fof(f146,plain,(
% 4.92/1.22 ![X0,X1,X2]: (ifeq(equalish(multiply(X0,X1),X2),true,product(X0,X1,X2),true)=true)),
% 4.92/1.22 inference(forward_demodulation,[status(thm)],[f11,f135])).
% 4.92/1.22 fof(f319,plain,(
% 4.92/1.22 ![X0]: (ifeq(true,true,ifeq(product(X0,sF1_fnc,identity),true,product(X0,identity,a),true),true)=true)),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f26,f63])).
% 4.92/1.22 fof(f323,plain,(
% 4.92/1.22 ![X0,X1,X2]: (ifeq(true,true,ifeq(product(X0,X1,identity),true,product(X0,multiply(X1,X2),X2),true),true)=true)),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f14,f63])).
% 4.92/1.22 fof(f325,plain,(
% 4.92/1.22 ![X0,X1]: (ifeq(product(b,X0,X1),true,ifeq(true,true,product(sF2_fnc,X1,X0),true),true)=true)),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f25,f63])).
% 4.92/1.22 fof(f326,plain,(
% 4.92/1.22 ![X0,X1,X2]: (ifeq(product(X0,X1,X2),true,ifeq(true,true,product(inverse(X0),X2,X1),true),true)=true)),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f13,f63])).
% 4.92/1.22 fof(f335,plain,(
% 4.92/1.22 ![X0]: (ifeq(product(X0,sF1_fnc,identity),true,product(X0,identity,a),true)=true)),
% 4.92/1.22 inference(forward_demodulation,[status(thm)],[f11,f319])).
% 4.92/1.22 fof(f339,plain,(
% 4.92/1.22 ![X0,X1,X2]: (ifeq(product(X0,X1,identity),true,product(X0,multiply(X1,X2),X2),true)=true)),
% 4.92/1.22 inference(forward_demodulation,[status(thm)],[f11,f323])).
% 4.92/1.22 fof(f341,plain,(
% 4.92/1.22 ![X0,X1]: (ifeq(product(b,X0,X1),true,product(sF2_fnc,X1,X0),true)=true)),
% 4.92/1.22 inference(forward_demodulation,[status(thm)],[f11,f325])).
% 4.92/1.22 fof(f342,plain,(
% 4.92/1.22 ![X0,X1,X2]: (ifeq(product(X0,X1,X2),true,product(inverse(X0),X2,X1),true)=true)),
% 4.92/1.22 inference(forward_demodulation,[status(thm)],[f11,f326])).
% 4.92/1.22 fof(f349,plain,(
% 4.92/1.22 ![X0,X1,X2]: (ifeq(true,true,ifeq(product(X0,identity,X1),true,product(X0,X2,multiply(X1,X2)),true),true)=true)),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f12,f64])).
% 4.92/1.22 fof(f363,plain,(
% 4.92/1.22 ![X0,X1,X2]: (ifeq(product(X0,identity,X1),true,product(X0,X2,multiply(X1,X2)),true)=true)),
% 4.92/1.22 inference(forward_demodulation,[status(thm)],[f11,f349])).
% 4.92/1.22 fof(f5301,plain,(
% 4.92/1.22 ifeq(true,true,product(inverse(sF1_fnc),identity,a),true)=true),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f13,f335])).
% 4.92/1.22 fof(f5310,plain,(
% 4.92/1.22 product(inverse(sF1_fnc),identity,a)=true),
% 4.92/1.22 inference(forward_demodulation,[status(thm)],[f11,f5301])).
% 4.92/1.22 fof(f5329,plain,(
% 4.92/1.22 ifeq(true,true,product(inverse(sF1_fnc),identity,b),true)=true),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f5310,f141])).
% 4.92/1.22 fof(f5400,plain,(
% 4.92/1.22 product(inverse(sF1_fnc),identity,b)=true),
% 4.92/1.22 inference(forward_demodulation,[status(thm)],[f11,f5329])).
% 4.92/1.22 fof(f5981,plain,(
% 4.92/1.22 ![X0]: (ifeq(true,true,product(sF2_fnc,multiply(b,X0),X0),true)=true)),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f25,f339])).
% 4.92/1.22 fof(f6006,plain,(
% 4.92/1.22 ![X0]: (product(sF2_fnc,multiply(b,X0),X0)=true)),
% 4.92/1.22 inference(forward_demodulation,[status(thm)],[f11,f5981])).
% 4.92/1.22 fof(f6626,plain,(
% 4.92/1.22 ![X0]: (ifeq(true,true,product(inverse(sF2_fnc),X0,multiply(b,X0)),true)=true)),
% 4.92/1.22 inference(paramodulation,[status(thm)],[f6006,f342])).
% 4.92/1.22 fof(f6682,plain,(
% 4.92/1.22 ![X0]: (product(inverse(sF2_fnc),X0,multiply(b,X0))=true)),
% 4.92/1.22 inference(forward_demodulation,[status(thm)],[f11,f6626])).
% 6.44/1.27 fof(f7975,plain,(
% 6.44/1.27 ![X0]: (ifeq(true,true,product(inverse(sF1_fnc),X0,multiply(b,X0)),true)=true)),
% 6.44/1.27 inference(paramodulation,[status(thm)],[f5400,f363])).
% 6.44/1.27 fof(f8011,plain,(
% 6.44/1.27 ![X0]: (product(inverse(sF1_fnc),X0,multiply(b,X0))=true)),
% 6.44/1.27 inference(forward_demodulation,[status(thm)],[f11,f7975])).
% 6.44/1.27 fof(f12406,plain,(
% 6.44/1.27 ifeq(true,true,equalish(multiply(b,sF2_fnc),identity),true)=true),
% 6.44/1.27 inference(paramodulation,[status(thm)],[f6682,f35])).
% 6.44/1.27 fof(f12521,plain,(
% 6.44/1.27 equalish(multiply(b,sF2_fnc),identity)=true),
% 6.44/1.27 inference(forward_demodulation,[status(thm)],[f11,f12406])).
% 6.44/1.27 fof(f12718,plain,(
% 6.44/1.27 ifeq(true,true,product(b,sF2_fnc,identity),true)=true),
% 6.44/1.27 inference(paramodulation,[status(thm)],[f12521,f146])).
% 6.44/1.27 fof(f12732,plain,(
% 6.44/1.27 product(b,sF2_fnc,identity)=true),
% 6.44/1.27 inference(forward_demodulation,[status(thm)],[f11,f12718])).
% 6.44/1.27 fof(f12882,plain,(
% 6.44/1.27 ifeq(true,true,product(sF2_fnc,identity,sF2_fnc),true)=true),
% 6.44/1.27 inference(paramodulation,[status(thm)],[f12732,f341])).
% 6.44/1.27 fof(f12975,plain,(
% 6.44/1.27 product(sF2_fnc,identity,sF2_fnc)=true),
% 6.44/1.27 inference(forward_demodulation,[status(thm)],[f11,f12882])).
% 6.44/1.27 fof(f19634,plain,(
% 6.44/1.27 ifeq(true,true,equalish(multiply(b,sF1_fnc),identity),true)=true),
% 6.44/1.27 inference(paramodulation,[status(thm)],[f8011,f35])).
% 6.44/1.27 fof(f19764,plain,(
% 6.44/1.27 equalish(multiply(b,sF1_fnc),identity)=true),
% 6.44/1.27 inference(forward_demodulation,[status(thm)],[f11,f19634])).
% 6.44/1.27 fof(f19911,plain,(
% 6.44/1.27 ifeq(true,true,product(b,sF1_fnc,identity),true)=true),
% 6.44/1.27 inference(paramodulation,[status(thm)],[f19764,f146])).
% 6.44/1.27 fof(f19925,plain,(
% 6.44/1.27 product(b,sF1_fnc,identity)=true),
% 6.44/1.27 inference(forward_demodulation,[status(thm)],[f11,f19911])).
% 6.44/1.27 fof(f19933,plain,(
% 6.44/1.27 ifeq(true,true,product(sF2_fnc,identity,sF1_fnc),true)=true),
% 6.44/1.27 inference(paramodulation,[status(thm)],[f19925,f341])).
% 6.44/1.27 fof(f20035,plain,(
% 6.44/1.27 product(sF2_fnc,identity,sF1_fnc)=true),
% 6.44/1.27 inference(forward_demodulation,[status(thm)],[f11,f19933])).
% 6.44/1.27 fof(f20153,plain,(
% 6.44/1.27 ifeq(product(sF2_fnc,identity,sF2_fnc),true,ifeq(true,true,sF0_fnc,true),true)=true),
% 6.44/1.27 inference(paramodulation,[status(thm)],[f20035,f33])).
% 6.44/1.27 fof(f20246,plain,(
% 6.44/1.27 ifeq(true,true,ifeq(true,true,sF0_fnc,true),true)=true),
% 6.44/1.27 inference(forward_demodulation,[status(thm)],[f12975,f20153])).
% 6.44/1.27 fof(f20247,plain,(
% 6.44/1.27 ifeq(true,true,sF0_fnc,true)=true),
% 6.44/1.27 inference(forward_demodulation,[status(thm)],[f11,f20246])).
% 6.44/1.27 fof(f20248,plain,(
% 6.44/1.27 sF0_fnc=true),
% 6.44/1.27 inference(forward_demodulation,[status(thm)],[f11,f20247])).
% 6.44/1.27 fof(f20249,plain,(
% 6.44/1.27 $false),
% 6.44/1.27 inference(forward_subsumption_resolution,[status(thm)],[f20248,f24])).
% 6.44/1.27 % SZS output end CNFRefutation for theBenchmark.p
% 6.44/1.33 % Elapsed time: 0.955028 seconds
% 6.44/1.33 % CPU time: 7.116889 seconds
% 6.44/1.33 % Total memory used: 195.836 MB
% 6.44/1.33 % Net memory used: 193.794 MB
%------------------------------------------------------------------------------