%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : RNG039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 02:05:12 PM UTC 2026
% Result : Unsatisfiable 3.51s 0.98s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n018.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 04:16:58 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.47 % Drodi V4.1.1
% 3.51/0.98 % Refutation found
% 3.51/0.98 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.51/0.98 % SZS output start CNFRefutation for theBenchmark
% 3.51/0.98 fof(f1,axiom,(
% 3.51/0.98 (![X]: (sum(additive_identity,X,X) ))),
% 3.51/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.51/0.98 fof(f3,axiom,(
% 3.51/0.98 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 3.51/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.51/0.98 fof(f16,axiom,(
% 3.51/0.98 (![X,Y,U,V]: (( ~ sum(X,Y,U)| ~ sum(X,Y,V)| U = V ) ))),
% 3.51/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.51/0.98 fof(f17,axiom,(
% 3.51/0.98 (![X,Y,U,V]: (( ~ product(X,Y,U)| ~ product(X,Y,V)| U = V ) ))),
% 3.51/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.51/0.98 fof(f18,axiom,(
% 3.51/0.98 (![A,B]: (sum(A,add(A,B),B) ))),
% 3.51/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.51/0.98 fof(f22,axiom,(
% 3.51/0.98 (![A]: (add(A,A) = additive_identity ))),
% 3.51/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.51/0.98 fof(f23,axiom,(
% 3.51/0.98 (![A]: (multiply(A,A) = A ))),
% 3.51/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.51/0.98 fof(f25,axiom,(
% 3.51/0.98 multiply(b,a) = d ),
% 3.51/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.51/0.98 fof(f29,axiom,(
% 3.51/0.98 product(c,b,c) ),
% 3.51/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.51/0.98 fof(f32,axiom,(
% 3.51/0.98 (![A,B]: (product(a,multiply(b,A),multiply(B,A)) ))),
% 3.51/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.51/0.98 fof(f48,axiom,(
% 3.51/0.98 product(c,a,multiply(a,d)) ),
% 3.51/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.51/0.98 fof(f53,axiom,(
% 3.51/0.98 product(add(a,b),b,add(c,b)) ),
% 3.51/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.51/0.98 fof(f56,axiom,(
% 3.51/0.98 product(add(a,b),a,add(a,d)) ),
% 3.51/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.51/0.98 fof(f60,negated_conjecture,(
% 3.51/0.98 c != d ),
% 3.51/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.51/0.98 fof(f61,plain,(
% 3.51/0.98 ![X0]: (sum(additive_identity,X0,X0))),
% 3.51/0.98 inference(cnf_transformation,[status(thm)],[f1])).
% 3.51/0.98 fof(f63,plain,(
% 3.51/0.98 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 3.51/0.98 inference(cnf_transformation,[status(thm)],[f3])).
% 3.51/0.98 fof(f84,plain,(
% 3.51/0.98 ![U,V]: ((![X,Y]: (~sum(X,Y,U)|~sum(X,Y,V)))|U=V)),
% 3.51/0.98 inference(miniscoping,[status(thm)],[f16])).
% 3.51/0.98 fof(f85,plain,(
% 3.51/0.98 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X0,X1,X3)|X2=X3)),
% 3.51/0.98 inference(cnf_transformation,[status(thm)],[f84])).
% 3.51/0.98 fof(f86,plain,(
% 3.51/0.98 ![U,V]: ((![X,Y]: (~product(X,Y,U)|~product(X,Y,V)))|U=V)),
% 3.51/0.98 inference(miniscoping,[status(thm)],[f17])).
% 3.51/0.98 fof(f87,plain,(
% 3.51/0.98 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 3.51/0.98 inference(cnf_transformation,[status(thm)],[f86])).
% 3.51/0.98 fof(f88,plain,(
% 3.51/0.98 ![X0,X1]: (sum(X0,add(X0,X1),X1))),
% 3.51/0.98 inference(cnf_transformation,[status(thm)],[f18])).
% 3.51/0.98 fof(f92,plain,(
% 3.51/0.98 ![X0]: (add(X0,X0)=additive_identity)),
% 3.51/0.98 inference(cnf_transformation,[status(thm)],[f22])).
% 3.51/0.98 fof(f93,plain,(
% 3.51/0.98 ![X0]: (multiply(X0,X0)=X0)),
% 3.51/0.98 inference(cnf_transformation,[status(thm)],[f23])).
% 3.51/0.98 fof(f95,plain,(
% 3.51/0.98 multiply(b,a)=d),
% 3.51/0.98 inference(cnf_transformation,[status(thm)],[f25])).
% 3.51/0.98 fof(f99,plain,(
% 3.51/0.98 product(c,b,c)),
% 3.51/0.98 inference(cnf_transformation,[status(thm)],[f29])).
% 3.51/0.98 fof(f102,plain,(
% 3.51/0.98 ![X0,X1]: (product(a,multiply(b,X0),multiply(X1,X0)))),
% 3.51/0.98 inference(cnf_transformation,[status(thm)],[f32])).
% 3.51/0.98 fof(f118,plain,(
% 3.51/0.98 product(c,a,multiply(a,d))),
% 3.51/0.98 inference(cnf_transformation,[status(thm)],[f48])).
% 3.51/0.98 fof(f123,plain,(
% 3.51/0.98 product(add(a,b),b,add(c,b))),
% 3.51/0.98 inference(cnf_transformation,[status(thm)],[f53])).
% 3.51/0.98 fof(f126,plain,(
% 3.51/0.98 product(add(a,b),a,add(a,d))),
% 3.51/0.98 inference(cnf_transformation,[status(thm)],[f56])).
% 3.51/0.98 fof(f130,plain,(
% 3.51/0.98 ~c=d),
% 3.51/0.98 inference(cnf_transformation,[status(thm)],[f60])).
% 3.51/0.98 fof(f170,plain,(
% 3.51/0.98 ![X0,X1]: (~sum(additive_identity,X0,X1)|X1=X0)),
% 3.51/0.98 inference(resolution,[status(thm)],[f85,f61])).
% 3.51/0.98 fof(f181,plain,(
% 3.51/0.98 ![X0]: (X0=add(additive_identity,X0))),
% 3.51/0.98 inference(resolution,[status(thm)],[f170,f88])).
% 3.51/0.98 fof(f490,plain,(
% 3.51/0.98 ![X0]: (~product(c,b,X0)|X0=c)),
% 3.51/0.98 inference(resolution,[status(thm)],[f87,f99])).
% 3.51/0.98 fof(f496,plain,(
% 3.51/0.98 ![X0,X1,X2]: (~product(X0,X1,X2)|X2=multiply(X0,X1))),
% 3.51/0.98 inference(resolution,[status(thm)],[f87,f63])).
% 3.51/0.98 fof(f518,plain,(
% 3.51/0.98 product(a,multiply(b,a),d)),
% 3.51/0.98 inference(paramodulation,[status(thm)],[f95,f102])).
% 3.51/0.99 fof(f520,plain,(
% 3.51/0.99 ![X0]: (product(a,multiply(b,X0),X0))),
% 3.51/0.99 inference(paramodulation,[status(thm)],[f93,f102])).
% 3.51/0.99 fof(f521,plain,(
% 3.51/0.99 product(a,d,d)),
% 3.51/0.99 inference(forward_demodulation,[status(thm)],[f95,f518])).
% 3.51/0.99 fof(f536,plain,(
% 3.51/0.99 multiply(c,b)=c),
% 3.51/0.99 inference(resolution,[status(thm)],[f490,f63])).
% 3.51/0.99 fof(f616,plain,(
% 3.51/0.99 d=multiply(a,d)),
% 3.51/0.99 inference(resolution,[status(thm)],[f496,f521])).
% 3.51/0.99 fof(f617,plain,(
% 3.51/0.99 ![X0,X1]: (multiply(X0,X1)=multiply(a,multiply(b,X1)))),
% 3.51/0.99 inference(resolution,[status(thm)],[f496,f102])).
% 3.51/0.99 fof(f630,plain,(
% 3.51/0.99 product(c,a,d)),
% 3.51/0.99 inference(backward_demodulation,[status(thm)],[f616,f118])).
% 3.51/0.99 fof(f647,plain,(
% 3.51/0.99 d=multiply(c,a)),
% 3.51/0.99 inference(resolution,[status(thm)],[f630,f496])).
% 3.51/0.99 fof(f759,plain,(
% 3.51/0.99 ![X0]: (X0=multiply(a,multiply(b,X0)))),
% 3.51/0.99 inference(resolution,[status(thm)],[f520,f496])).
% 3.51/0.99 fof(f765,plain,(
% 3.51/0.99 ![X0,X1]: (multiply(X0,X1)=X1)),
% 3.51/0.99 inference(backward_demodulation,[status(thm)],[f759,f617])).
% 3.51/0.99 fof(f767,plain,(
% 3.51/0.99 d=a),
% 3.51/0.99 inference(backward_demodulation,[status(thm)],[f765,f647])).
% 3.51/0.99 fof(f768,plain,(
% 3.51/0.99 b=c),
% 3.51/0.99 inference(backward_demodulation,[status(thm)],[f765,f536])).
% 3.51/0.99 fof(f783,plain,(
% 3.51/0.99 ![X0,X1,X2]: (~product(X0,X1,X2)|X2=X1)),
% 3.51/0.99 inference(backward_demodulation,[status(thm)],[f765,f496])).
% 3.51/0.99 fof(f839,plain,(
% 3.51/0.99 product(add(a,b),a,add(d,d))),
% 3.51/0.99 inference(backward_demodulation,[status(thm)],[f767,f126])).
% 3.51/0.99 fof(f842,plain,(
% 3.51/0.99 product(add(d,b),b,add(c,b))),
% 3.51/0.99 inference(backward_demodulation,[status(thm)],[f767,f123])).
% 3.51/0.99 fof(f920,plain,(
% 3.51/0.99 product(add(d,b),a,add(d,d))),
% 3.51/0.99 inference(forward_demodulation,[status(thm)],[f767,f839])).
% 3.51/0.99 fof(f921,plain,(
% 3.51/0.99 product(add(d,c),a,add(d,d))),
% 3.51/0.99 inference(forward_demodulation,[status(thm)],[f768,f920])).
% 3.51/0.99 fof(f922,plain,(
% 3.51/0.99 product(add(d,c),d,add(d,d))),
% 3.51/0.99 inference(forward_demodulation,[status(thm)],[f767,f921])).
% 3.51/0.99 fof(f923,plain,(
% 3.51/0.99 product(add(d,c),d,additive_identity)),
% 3.51/0.99 inference(forward_demodulation,[status(thm)],[f92,f922])).
% 3.51/0.99 fof(f932,plain,(
% 3.51/0.99 product(add(d,c),b,add(c,b))),
% 3.51/0.99 inference(forward_demodulation,[status(thm)],[f768,f842])).
% 3.51/0.99 fof(f933,plain,(
% 3.51/0.99 product(add(d,c),c,add(c,b))),
% 3.51/0.99 inference(forward_demodulation,[status(thm)],[f768,f932])).
% 3.51/0.99 fof(f934,plain,(
% 3.51/0.99 product(add(d,c),c,add(c,c))),
% 3.51/0.99 inference(forward_demodulation,[status(thm)],[f768,f933])).
% 3.51/0.99 fof(f935,plain,(
% 3.51/0.99 product(add(d,c),c,additive_identity)),
% 3.51/0.99 inference(forward_demodulation,[status(thm)],[f92,f934])).
% 3.51/0.99 fof(f970,plain,(
% 3.51/0.99 additive_identity=d),
% 3.51/0.99 inference(resolution,[status(thm)],[f923,f783])).
% 3.51/0.99 fof(f975,plain,(
% 3.51/0.99 ![X0]: (X0=add(d,X0))),
% 3.51/0.99 inference(backward_demodulation,[status(thm)],[f970,f181])).
% 3.51/0.99 fof(f982,plain,(
% 3.51/0.99 product(add(d,c),c,d)),
% 3.51/0.99 inference(backward_demodulation,[status(thm)],[f970,f935])).
% 3.51/0.99 fof(f998,plain,(
% 3.51/0.99 product(c,c,d)),
% 3.51/0.99 inference(forward_demodulation,[status(thm)],[f975,f982])).
% 3.51/0.99 fof(f1103,plain,(
% 3.51/0.99 d=c),
% 3.51/0.99 inference(resolution,[status(thm)],[f998,f783])).
% 3.51/0.99 fof(f1105,plain,(
% 3.51/0.99 $false),
% 3.51/0.99 inference(forward_subsumption_resolution,[status(thm)],[f1103,f130])).
% 3.51/0.99 % SZS output end CNFRefutation for theBenchmark.p
% 3.51/1.01 % Elapsed time: 0.537953 seconds
% 3.51/1.01 % CPU time: 3.834749 seconds
% 3.51/1.01 % Total memory used: 83.213 MB
% 3.51/1.01 % Net memory used: 80.257 MB
%------------------------------------------------------------------------------