%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ROB015-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 : Sun Sep 27 08:26:58 AM UTC 2026
% Result : Unsatisfiable 86.37s 12.41s
% Output : CNFRefutation 86.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 38 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 51 ( 3 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ifeq_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq4(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c_1,plain,
ifeq4(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom]) ).
fof(ifeq_axiom_001,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq3(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom_001) ).
cnf(c_2,plain,
ifeq3(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom_001]) ).
fof(ifeq_axiom_002,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq2(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom_002) ).
cnf(c_3,plain,
ifeq2(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom_002]) ).
fof(commutativity_of_add,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_add) ).
cnf(c_5,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutativity_of_add]) ).
fof(lemma_3_2,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq4(negate(add(VAR_0,negate(add(VAR_1,VAR_2)))),negate(add(VAR_1,negate(add(VAR_0,VAR_2)))),VAR_0,VAR_1) = VAR_1,
file('theBenchmark.p',lemma_3_2) ).
cnf(c_12,plain,
ifeq4(negate(add(A,negate(add(B,C)))),negate(add(B,negate(add(A,C)))),A,B) = B,
inference(clausify,[status(thm)],[lemma_3_2]) ).
fof(lemma_3_4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : ifeq2(positive_integer(VAR_0),true,ifeq4(negate(add(VAR_1,negate(VAR_2))),VAR_3,negate(add(VAR_1,negate(add(VAR_2,multiply(VAR_0,add(VAR_1,VAR_3)))))),VAR_3),VAR_3) = VAR_3,
file('theBenchmark.p',lemma_3_4) ).
cnf(c_13,plain,
ifeq2(positive_integer(A),true,ifeq4(negate(add(B,negate(C))),D,negate(add(B,negate(add(C,multiply(A,add(B,D)))))),D),D) = D,
inference(clausify,[status(thm)],[lemma_3_4]) ).
fof(condition,axiom,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
file('theBenchmark.p',condition) ).
cnf(c_14,plain,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
inference(clausify,[status(thm)],[condition]) ).
fof(k_positive,axiom,
positive_integer(k) = true,
file('theBenchmark.p',k_positive) ).
cnf(c_15,plain,
positive_integer(k) = true,
inference(clausify,[status(thm)],[k_positive]) ).
fof(base_step,axiom,
ifeq3(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e),a,b) = b,
file('theBenchmark.p',base_step) ).
cnf(c_16,plain,
ifeq3(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e),a,b) = b,
inference(clausify,[status(thm)],[base_step]) ).
fof(goal,axiom,
a != b,
file('theBenchmark.p',goal) ).
cnf(c_18,plain,
a != b,
inference(clausify,[status(thm)],[goal]) ).
cnf(c_31,plain,
ifeq4(negate(add(A,negate(add(B,C)))),negate(add(C,negate(add(A,B)))),A,C) = C,
inference(paramod,[status(thm)],[c_5,c_12]) ).
cnf(c_41,plain,
ifeq2(positive_integer(A),true,negate(add(B,negate(add(C,multiply(A,add(B,negate(add(B,negate(C))))))))),negate(add(B,negate(C)))) = negate(add(B,negate(C))),
inference(paramod,[status(thm)],[c_1,c_13]) ).
cnf(c_655,plain,
ifeq4(negate(add(negate(add(A,B)),C)),negate(add(B,negate(add(C,A)))),C,B) = B,
inference(paramod,[status(thm)],[c_5,c_31]) ).
cnf(c_11516,plain,
ifeq2(true,true,negate(add(A,negate(add(B,multiply(k,add(A,negate(add(A,negate(B))))))))),negate(add(A,negate(B)))) = negate(add(A,negate(B))),
inference(paramod,[status(thm)],[c_15,c_41]) ).
cnf(c_3106,plain,
negate(add(A,negate(add(B,multiply(k,add(A,negate(add(A,negate(B))))))))) = negate(add(A,negate(B))),
inference(paramod,[status(thm)],[c_3,c_11516]) ).
cnf(c_7797,plain,
negate(add(A,negate(add(B,multiply(k,add(A,negate(add(negate(B),A)))))))) = negate(add(A,negate(B))),
inference(paramod,[status(thm)],[c_5,c_3106]) ).
cnf(c_11517,plain,
negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(negate(add(d,negate(e))),d)))))) = negate(add(negate(add(d,negate(e))),negate(e))),
inference(paramod,[status(thm)],[c_14,c_7797]) ).
cnf(c_11518,plain,
negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))) = negate(add(negate(add(d,negate(e))),negate(e))),
inference(paramod,[status(thm)],[c_5,c_11517]) ).
cnf(c_11519,plain,
negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))) = negate(add(negate(e),negate(add(d,negate(e))))),
inference(paramod,[status(thm)],[c_5,c_11518]) ).
cnf(c_9650,plain,
negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))) = d,
inference(paramod,[status(thm)],[c_14,c_11519]) ).
cnf(c_11520,plain,
ifeq4(d,negate(add(negate(e),negate(add(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),d)))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)) = negate(e),
inference(paramod,[status(thm)],[c_9650,c_655]) ).
cnf(c_11521,plain,
ifeq4(d,negate(add(negate(e),negate(add(d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)) = negate(e),
inference(paramod,[status(thm)],[c_5,c_11520]) ).
cnf(c_11522,plain,
ifeq4(d,negate(add(negate(e),negate(add(d,negate(e))))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)) = negate(e),
inference(paramod,[status(thm)],[c_3106,c_11521]) ).
cnf(c_11523,plain,
ifeq4(d,d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)) = negate(e),
inference(paramod,[status(thm)],[c_14,c_11522]) ).
cnf(c_11495,plain,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) = negate(e),
inference(paramod,[status(thm)],[c_1,c_11523]) ).
cnf(c_11524,plain,
ifeq3(negate(e),negate(e),a,b) = b,
inference(paramod,[status(thm)],[c_11495,c_16]) ).
cnf(c_11525,plain,
a = b,
inference(paramod,[status(thm)],[c_2,c_11524]) ).
cnf(c_11515,plain,
$false,
inference(resolve,[status(thm)],[c_18,c_11525]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB015-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 06:14:51 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 981002 was started by sandbox2 on n004,
% 0.11/0.38 % Sat Sep 26 06:14:51 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.38
% 0.16/0.38 % From the command line: assign(max_seconds, 300).
% 86.37/12.41
% 86.37/12.41 % SZS status Unsatisfiable for theBenchmark
% 86.37/12.41
% 86.37/12.41 % Proof 1 at 3.11 (+ 0.53) seconds.
% 86.37/12.41 % Length of proof is 18.
% 86.37/12.41 % Level of proof is 6.
% 86.37/12.41 % Maximum clause weight is 30.000.
% 86.37/12.41 % Given clauses 203.
% 86.37/12.41
% 86.37/12.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------