%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : RNG004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 02:05:05 PM UTC 2026
% Result : Unsatisfiable 3.25s 0.86s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n016.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 04:14:52 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 3.25/0.86 % Refutation found
% 3.25/0.86 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.25/0.86 % SZS output start CNFRefutation for theBenchmark
% 3.25/0.86 fof(f2,axiom,(
% 3.25/0.86 (![X]: (sum(X,additive_identity,X) ))),
% 3.25/0.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.25/0.86 fof(f3,axiom,(
% 3.25/0.86 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 3.25/0.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.25/0.86 fof(f5,axiom,(
% 3.25/0.86 (![X]: (sum(additive_inverse(X),X,additive_identity) ))),
% 3.25/0.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.25/0.86 fof(f6,axiom,(
% 3.25/0.86 (![X]: (sum(X,additive_inverse(X),additive_identity) ))),
% 3.25/0.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.25/0.86 fof(f12,axiom,(
% 3.25/0.86 (![X,Y,V1,Z,V2,V3,V4]: (( ~ product(X,Y,V1)| ~ product(X,Z,V2)| ~ sum(Y,Z,V3)| ~ product(X,V3,V4)| sum(V1,V2,V4) ) ))),
% 3.25/0.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.25/0.86 fof(f14,axiom,(
% 3.25/0.86 (![Y,X,V1,Z,V2,V3,V4]: (( ~ product(Y,X,V1)| ~ product(Z,X,V2)| ~ sum(Y,Z,V3)| ~ product(V3,X,V4)| sum(V1,V2,V4) ) ))),
% 3.25/0.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.25/0.86 fof(f18,axiom,(
% 3.25/0.86 (![X,Y,Z,W]: (( ~ sum(X,Y,Z)| ~ sum(X,W,Z)| Y = W ) ))),
% 3.25/0.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.25/0.86 fof(f19,axiom,(
% 3.25/0.86 (![X,Y,Z,W]: (( ~ sum(X,Y,Z)| ~ sum(W,Y,Z)| X = W ) ))),
% 3.25/0.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.25/0.86 fof(f20,hypothesis,(
% 3.25/0.86 product(a,b,c) ),
% 3.25/0.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.25/0.86 fof(f21,hypothesis,(
% 3.25/0.86 product(additive_inverse(a),additive_inverse(b),d) ),
% 3.25/0.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.25/0.86 fof(f22,negated_conjecture,(
% 3.25/0.86 c != d ),
% 3.25/0.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.25/0.86 fof(f24,plain,(
% 3.25/0.86 ![X0]: (sum(X0,additive_identity,X0))),
% 3.25/0.86 inference(cnf_transformation,[status(thm)],[f2])).
% 3.25/0.86 fof(f25,plain,(
% 3.25/0.86 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 3.25/0.86 inference(cnf_transformation,[status(thm)],[f3])).
% 3.25/0.86 fof(f27,plain,(
% 3.25/0.86 ![X0]: (sum(additive_inverse(X0),X0,additive_identity))),
% 3.25/0.86 inference(cnf_transformation,[status(thm)],[f5])).
% 3.25/0.86 fof(f28,plain,(
% 3.25/0.86 ![X0]: (sum(X0,additive_inverse(X0),additive_identity))),
% 3.25/0.86 inference(cnf_transformation,[status(thm)],[f6])).
% 3.25/0.86 fof(f38,plain,(
% 3.25/0.86 ![V1,V2,V4]: ((![X,V3]: ((![Y,Z]: ((~product(X,Y,V1)|~product(X,Z,V2))|~sum(Y,Z,V3)))|~product(X,V3,V4)))|sum(V1,V2,V4))),
% 3.25/0.86 inference(miniscoping,[status(thm)],[f12])).
% 3.25/0.86 fof(f39,plain,(
% 3.25/0.86 ![X0,X1,X2,X3,X4,X5,X6]: (~product(X0,X1,X2)|~product(X0,X3,X4)|~sum(X1,X3,X5)|~product(X0,X5,X6)|sum(X2,X4,X6))),
% 3.25/0.86 inference(cnf_transformation,[status(thm)],[f38])).
% 3.25/0.86 fof(f42,plain,(
% 3.25/0.86 ![V1,V2,V4]: ((![X,V3]: ((![Y,Z]: ((~product(Y,X,V1)|~product(Z,X,V2))|~sum(Y,Z,V3)))|~product(V3,X,V4)))|sum(V1,V2,V4))),
% 3.25/0.86 inference(miniscoping,[status(thm)],[f14])).
% 3.25/0.86 fof(f43,plain,(
% 3.25/0.86 ![X0,X1,X2,X3,X4,X5,X6]: (~product(X0,X1,X2)|~product(X3,X1,X4)|~sum(X0,X3,X5)|~product(X5,X1,X6)|sum(X2,X4,X6))),
% 3.25/0.86 inference(cnf_transformation,[status(thm)],[f42])).
% 3.25/0.86 fof(f50,plain,(
% 3.25/0.86 ![Y,W]: ((![X,Z]: (~sum(X,Y,Z)|~sum(X,W,Z)))|Y=W)),
% 3.25/0.86 inference(miniscoping,[status(thm)],[f18])).
% 3.25/0.86 fof(f51,plain,(
% 3.25/0.86 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X0,X3,X2)|X1=X3)),
% 3.25/0.86 inference(cnf_transformation,[status(thm)],[f50])).
% 3.25/0.86 fof(f52,plain,(
% 3.25/0.86 ![X,W]: ((![Y,Z]: (~sum(X,Y,Z)|~sum(W,Y,Z)))|X=W)),
% 3.25/0.86 inference(miniscoping,[status(thm)],[f19])).
% 3.25/0.86 fof(f53,plain,(
% 3.25/0.86 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X3,X1,X2)|X0=X3)),
% 3.25/0.86 inference(cnf_transformation,[status(thm)],[f52])).
% 3.25/0.86 fof(f54,plain,(
% 3.25/0.86 product(a,b,c)),
% 3.25/0.86 inference(cnf_transformation,[status(thm)],[f20])).
% 3.25/0.86 fof(f55,plain,(
% 3.25/0.86 product(additive_inverse(a),additive_inverse(b),d)),
% 3.25/0.86 inference(cnf_transformation,[status(thm)],[f21])).
% 3.25/0.86 fof(f56,plain,(
% 3.25/0.86 ~c=d),
% 3.25/0.86 inference(cnf_transformation,[status(thm)],[f22])).
% 3.25/0.86 fof(f139,plain,(
% 3.25/0.86 ![X0,X1,X2,X3]: (~product(a,X0,X1)|~sum(b,X0,X2)|~product(a,X2,X3)|sum(c,X1,X3))),
% 3.25/0.86 inference(resolution,[status(thm)],[f39,f54])).
% 3.25/0.86 fof(f172,plain,(
% 3.25/0.86 ![X0,X1,X2]: (~sum(b,X0,X1)|~product(a,X1,X2)|sum(c,multiply(a,X0),X2))),
% 3.25/0.86 inference(resolution,[status(thm)],[f139,f25])).
% 3.25/0.86 fof(f219,plain,(
% 3.25/0.86 ![X0,X1,X2,X3]: (~product(X0,additive_inverse(b),X1)|~sum(additive_inverse(a),X0,X2)|~product(X2,additive_inverse(b),X3)|sum(d,X1,X3))),
% 2.65/0.87 inference(resolution,[status(thm)],[f43,f55])).
% 2.65/0.87 fof(f234,plain,(
% 2.65/0.87 ![X0,X1]: (~sum(X0,X1,additive_identity)|additive_inverse(X0)=X1)),
% 2.65/0.87 inference(resolution,[status(thm)],[f51,f28])).
% 2.65/0.87 fof(f235,plain,(
% 2.65/0.87 ![X0,X1]: (~sum(X0,X1,X0)|additive_identity=X1)),
% 2.65/0.87 inference(resolution,[status(thm)],[f51,f24])).
% 2.65/0.87 fof(f258,plain,(
% 2.65/0.87 ![X0,X1,X2]: (~sum(additive_inverse(a),X0,X1)|~product(X1,additive_inverse(b),X2)|sum(d,multiply(X0,additive_inverse(b)),X2))),
% 2.65/0.87 inference(resolution,[status(thm)],[f219,f25])).
% 2.65/0.87 fof(f296,plain,(
% 2.65/0.87 ![X0,X1]: (~sum(X0,additive_inverse(X1),additive_identity)|X1=X0)),
% 2.65/0.87 inference(resolution,[status(thm)],[f53,f28])).
% 2.65/0.87 fof(f398,plain,(
% 2.65/0.87 ![X0]: (~product(a,additive_identity,X0)|sum(c,multiply(a,additive_inverse(b)),X0))),
% 2.65/0.87 inference(resolution,[status(thm)],[f172,f28])).
% 2.65/0.87 fof(f399,plain,(
% 2.65/0.87 ![X0]: (~product(a,b,X0)|sum(c,multiply(a,additive_identity),X0))),
% 2.65/0.87 inference(resolution,[status(thm)],[f172,f24])).
% 2.65/0.87 fof(f456,plain,(
% 2.65/0.87 sum(c,multiply(a,additive_identity),c)),
% 2.65/0.87 inference(resolution,[status(thm)],[f399,f54])).
% 2.65/0.87 fof(f465,plain,(
% 2.65/0.87 additive_identity=multiply(a,additive_identity)),
% 2.65/0.87 inference(resolution,[status(thm)],[f456,f235])).
% 2.65/0.87 fof(f475,plain,(
% 2.65/0.87 product(a,additive_identity,additive_identity)),
% 2.65/0.87 inference(paramodulation,[status(thm)],[f465,f25])).
% 2.65/0.87 fof(f547,plain,(
% 2.65/0.87 ![X0]: (~product(additive_identity,additive_inverse(b),X0)|sum(d,multiply(a,additive_inverse(b)),X0))),
% 2.65/0.87 inference(resolution,[status(thm)],[f258,f27])).
% 2.65/0.87 fof(f549,plain,(
% 2.65/0.87 ![X0]: (~product(additive_inverse(a),additive_inverse(b),X0)|sum(d,multiply(additive_identity,additive_inverse(b)),X0))),
% 2.65/0.87 inference(resolution,[status(thm)],[f258,f24])).
% 2.65/0.87 fof(f2390,plain,(
% 2.65/0.87 sum(c,multiply(a,additive_inverse(b)),additive_identity)),
% 2.65/0.87 inference(resolution,[status(thm)],[f398,f475])).
% 2.65/0.87 fof(f2739,plain,(
% 2.65/0.87 additive_inverse(c)=multiply(a,additive_inverse(b))),
% 2.65/0.87 inference(resolution,[status(thm)],[f2390,f234])).
% 2.65/0.87 fof(f2847,plain,(
% 2.65/0.87 ![X0]: (~product(additive_identity,additive_inverse(b),X0)|sum(d,additive_inverse(c),X0))),
% 2.65/0.87 inference(forward_demodulation,[status(thm)],[f2739,f547])).
% 2.65/0.87 fof(f2852,plain,(
% 2.65/0.87 sum(d,multiply(additive_identity,additive_inverse(b)),d)),
% 2.65/0.87 inference(resolution,[status(thm)],[f549,f55])).
% 2.65/0.87 fof(f3208,plain,(
% 2.65/0.87 additive_identity=multiply(additive_identity,additive_inverse(b))),
% 2.65/0.87 inference(resolution,[status(thm)],[f2852,f235])).
% 2.65/0.87 fof(f3230,plain,(
% 2.65/0.87 product(additive_identity,additive_inverse(b),additive_identity)),
% 2.65/0.87 inference(paramodulation,[status(thm)],[f3208,f25])).
% 2.65/0.87 fof(f3239,plain,(
% 2.65/0.87 sum(d,additive_inverse(c),additive_identity)),
% 2.65/0.87 inference(resolution,[status(thm)],[f3230,f2847])).
% 2.65/0.87 fof(f3261,plain,(
% 2.65/0.87 c=d),
% 2.65/0.87 inference(resolution,[status(thm)],[f3239,f296])).
% 2.65/0.87 fof(f3287,plain,(
% 2.65/0.87 $false),
% 2.65/0.87 inference(forward_subsumption_resolution,[status(thm)],[f3261,f56])).
% 2.65/0.87 % SZS output end CNFRefutation for theBenchmark.p
% 2.65/0.88 % Elapsed time: 0.528385 seconds
% 2.65/0.88 % CPU time: 3.787268 seconds
% 2.65/0.88 % Total memory used: 59.428 MB
% 2.65/0.88 % Net memory used: 56.620 MB
%------------------------------------------------------------------------------