0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n010.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 180
0.12/0.33	% DateTime   : Thu Aug 29 09:07:06 EDT 2019
0.12/0.34	% CPUTime    : 
0.50/0.70	% SZS status Unsatisfiable
0.50/0.70	
0.50/0.70	% SZS output start Proof
0.50/0.70	Take the following subset of the input axioms:
0.50/0.72	  fof(axiom_1, axiom, s0(d)=true).
0.50/0.72	  fof(axiom_12, axiom, ![X]: true=m0(a, X, a)).
0.50/0.72	  fof(axiom_14, axiom, ![X]: p0(b, X)=true).
0.50/0.72	  fof(axiom_20, axiom, true=l0(a)).
0.50/0.72	  fof(axiom_30, axiom, n0(e, e)=true).
0.50/0.72	  fof(ifeq_axiom, axiom, ![C, B, A]: B=ifeq(A, A, B, C)).
0.50/0.72	  fof(prove_this, negated_conjecture, r4(b)!=true).
0.50/0.72	  fof(rule_002, axiom, ![G, H]: ifeq(n0(H, G), true, l1(G, G), true)=true).
0.50/0.72	  fof(rule_023, axiom, true=ifeq(l0(a), true, ifeq(s0(d), true, m1(a, a, a), true), true)).
0.50/0.72	  fof(rule_110, axiom, ![C, D, B]: ifeq(m0(C, D, B), true, q1(B, B, B), true)=true).
0.50/0.72	  fof(rule_150, axiom, ![F, G]: ifeq(m1(G, G, F), true, p2(F, F, F), true)=true).
0.50/0.72	  fof(rule_165, axiom, ![J, A, I]: ifeq(p2(J, J, A), true, ifeq(q1(J, A, J), true, p2(I, I, I), true), true)=true).
0.50/0.72	  fof(rule_186, axiom, ![G, H]: true=ifeq(l1(H, G), true, q2(G, G, H), true)).
0.50/0.72	  fof(rule_240, axiom, ![E, F, D]: true=ifeq(p2(E, F, D), true, n3(D), true)).
0.50/0.72	  fof(rule_255, axiom, ![G, H, I]: ifeq(q2(I, G, H), true, ifeq(n0(I, G), true, q3(G, H), true), true)=true).
0.50/0.72	  fof(rule_298, axiom, ![G, H, J, I]: ifeq(q3(H, I), true, ifeq(n3(G), true, ifeq(p0(J, G), true, r4(G), true), true), true)=true).
0.50/0.72	
0.50/0.72	Now clausify the problem and encode Horn clauses using encoding 3 of
0.50/0.72	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.50/0.72	We repeatedly replace C & s=t => u=v by the two clauses:
0.50/0.72	  fresh(y, y, x1...xn) = u
0.50/0.72	  C => fresh(s, t, x1...xn) = v
0.50/0.72	where fresh is a fresh function symbol and x1..xn are the free
0.50/0.72	variables of u and v.
0.50/0.72	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.50/0.72	input problem has no model of domain size 1).
0.50/0.72	
0.50/0.72	The encoding turns the above axioms into the following unit equations and goals:
0.50/0.72	
0.50/0.72	Axiom 1 (rule_240): true = ifeq(p2(X, Y, Z), true, n3(Z), true).
0.50/0.72	Axiom 2 (rule_165): ifeq(p2(X, X, Y), true, ifeq(q1(X, Y, X), true, p2(Z, Z, Z), true), true) = true.
0.50/0.72	Axiom 3 (rule_255): ifeq(q2(X, Y, Z), true, ifeq(n0(X, Y), true, q3(Y, Z), true), true) = true.
0.50/0.72	Axiom 4 (rule_110): ifeq(m0(X, Y, Z), true, q1(Z, Z, Z), true) = true.
0.50/0.72	Axiom 5 (axiom_20): true = l0(a).
0.50/0.72	Axiom 6 (rule_186): true = ifeq(l1(X, Y), true, q2(Y, Y, X), true).
0.50/0.72	Axiom 7 (rule_150): ifeq(m1(X, X, Y), true, p2(Y, Y, Y), true) = true.
0.50/0.72	Axiom 8 (rule_002): ifeq(n0(X, Y), true, l1(Y, Y), true) = true.
0.50/0.72	Axiom 9 (axiom_14): p0(b, X) = true.
0.50/0.72	Axiom 10 (axiom_1): s0(d) = true.
0.50/0.72	Axiom 11 (rule_298): ifeq(q3(X, Y), true, ifeq(n3(Z), true, ifeq(p0(W, Z), true, r4(Z), true), true), true) = true.
0.50/0.72	Axiom 12 (ifeq_axiom): X = ifeq(Y, Y, X, Z).
0.50/0.72	Axiom 13 (axiom_30): n0(e, e) = true.
0.50/0.72	Axiom 14 (axiom_12): true = m0(a, X, a).
0.56/0.74	Axiom 15 (rule_023): true = ifeq(l0(a), true, ifeq(s0(d), true, m1(a, a, a), true), true).
0.56/0.74	
0.56/0.74	Goal 1 (prove_this): r4(b) = true.
0.56/0.74	Proof:
0.56/0.74	  r4(b)
0.56/0.74	= { by axiom 12 (ifeq_axiom) }
0.56/0.74	  ifeq(true, true, r4(b), true)
0.56/0.74	= { by axiom 9 (axiom_14) }
0.56/0.74	  ifeq(p0(b, b), true, r4(b), true)
0.56/0.74	= { by axiom 12 (ifeq_axiom) }
0.56/0.74	  ifeq(true, true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 1 (rule_240) }
0.56/0.74	  ifeq(ifeq(p2(b, b, b), true, n3(b), true), true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 12 (ifeq_axiom) }
0.56/0.74	  ifeq(ifeq(ifeq(true, true, p2(b, b, b), true), true, n3(b), true), true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 4 (rule_110) }
0.56/0.74	  ifeq(ifeq(ifeq(ifeq(m0(a, ?, a), true, q1(a, a, a), true), true, p2(b, b, b), true), true, n3(b), true), true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 14 (axiom_12) }
0.56/0.74	  ifeq(ifeq(ifeq(ifeq(true, true, q1(a, a, a), true), true, p2(b, b, b), true), true, n3(b), true), true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 12 (ifeq_axiom) }
0.56/0.74	  ifeq(ifeq(ifeq(q1(a, a, a), true, p2(b, b, b), true), true, n3(b), true), true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 12 (ifeq_axiom) }
0.56/0.74	  ifeq(ifeq(ifeq(true, true, ifeq(q1(a, a, a), true, p2(b, b, b), true), true), true, n3(b), true), true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 7 (rule_150) }
0.56/0.74	  ifeq(ifeq(ifeq(ifeq(m1(a, a, a), true, p2(a, a, a), true), true, ifeq(q1(a, a, a), true, p2(b, b, b), true), true), true, n3(b), true), true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 12 (ifeq_axiom) }
0.56/0.74	  ifeq(ifeq(ifeq(ifeq(ifeq(true, true, m1(a, a, a), true), true, p2(a, a, a), true), true, ifeq(q1(a, a, a), true, p2(b, b, b), true), true), true, n3(b), true), true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 12 (ifeq_axiom) }
0.56/0.74	  ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(true, true, m1(a, a, a), true), true), true, p2(a, a, a), true), true, ifeq(q1(a, a, a), true, p2(b, b, b), true), true), true, n3(b), true), true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 5 (axiom_20) }
0.56/0.74	  ifeq(ifeq(ifeq(ifeq(ifeq(l0(a), true, ifeq(true, true, m1(a, a, a), true), true), true, p2(a, a, a), true), true, ifeq(q1(a, a, a), true, p2(b, b, b), true), true), true, n3(b), true), true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 10 (axiom_1) }
0.56/0.74	  ifeq(ifeq(ifeq(ifeq(ifeq(l0(a), true, ifeq(s0(d), true, m1(a, a, a), true), true), true, p2(a, a, a), true), true, ifeq(q1(a, a, a), true, p2(b, b, b), true), true), true, n3(b), true), true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 15 (rule_023) }
0.56/0.74	  ifeq(ifeq(ifeq(ifeq(true, true, p2(a, a, a), true), true, ifeq(q1(a, a, a), true, p2(b, b, b), true), true), true, n3(b), true), true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 12 (ifeq_axiom) }
0.56/0.74	  ifeq(ifeq(ifeq(p2(a, a, a), true, ifeq(q1(a, a, a), true, p2(b, b, b), true), true), true, n3(b), true), true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 2 (rule_165) }
0.56/0.74	  ifeq(ifeq(true, true, n3(b), true), true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 12 (ifeq_axiom) }
0.56/0.74	  ifeq(n3(b), true, ifeq(p0(b, b), true, r4(b), true), true)
0.56/0.74	= { by axiom 12 (ifeq_axiom) }
0.56/0.74	  ifeq(true, true, ifeq(n3(b), true, ifeq(p0(b, b), true, r4(b), true), true), true)
0.56/0.74	= { by axiom 3 (rule_255) }
0.56/0.74	  ifeq(ifeq(q2(e, e, e), true, ifeq(n0(e, e), true, q3(e, e), true), true), true, ifeq(n3(b), true, ifeq(p0(b, b), true, r4(b), true), true), true)
0.56/0.74	= { by axiom 12 (ifeq_axiom) }
0.56/0.74	  ifeq(ifeq(ifeq(true, true, q2(e, e, e), true), true, ifeq(n0(e, e), true, q3(e, e), true), true), true, ifeq(n3(b), true, ifeq(p0(b, b), true, r4(b), true), true), true)
0.56/0.74	= { by axiom 8 (rule_002) }
0.56/0.74	  ifeq(ifeq(ifeq(ifeq(n0(e, e), true, l1(e, e), true), true, q2(e, e, e), true), true, ifeq(n0(e, e), true, q3(e, e), true), true), true, ifeq(n3(b), true, ifeq(p0(b, b), true, r4(b), true), true), true)
0.56/0.74	= { by axiom 13 (axiom_30) }
0.56/0.74	  ifeq(ifeq(ifeq(ifeq(true, true, l1(e, e), true), true, q2(e, e, e), true), true, ifeq(n0(e, e), true, q3(e, e), true), true), true, ifeq(n3(b), true, ifeq(p0(b, b), true, r4(b), true), true), true)
0.56/0.74	= { by axiom 12 (ifeq_axiom) }
0.56/0.74	  ifeq(ifeq(ifeq(l1(e, e), true, q2(e, e, e), true), true, ifeq(n0(e, e), true, q3(e, e), true), true), true, ifeq(n3(b), true, ifeq(p0(b, b), true, r4(b), true), true), true)
0.56/0.74	= { by axiom 6 (rule_186) }
0.56/0.74	  ifeq(ifeq(true, true, ifeq(n0(e, e), true, q3(e, e), true), true), true, ifeq(n3(b), true, ifeq(p0(b, b), true, r4(b), true), true), true)
0.56/0.74	= { by axiom 12 (ifeq_axiom) }
0.56/0.74	  ifeq(ifeq(n0(e, e), true, q3(e, e), true), true, ifeq(n3(b), true, ifeq(p0(b, b), true, r4(b), true), true), true)
0.56/0.74	= { by axiom 13 (axiom_30) }
0.56/0.74	  ifeq(ifeq(true, true, q3(e, e), true), true, ifeq(n3(b), true, ifeq(p0(b, b), true, r4(b), true), true), true)
0.56/0.74	= { by axiom 12 (ifeq_axiom) }
0.56/0.74	  ifeq(q3(e, e), true, ifeq(n3(b), true, ifeq(p0(b, b), true, r4(b), true), true), true)
0.56/0.74	= { by axiom 11 (rule_298) }
0.56/0.74	  true
0.56/0.74	% SZS output end Proof
0.56/0.74	
0.56/0.74	RESULT: Unsatisfiable (the axioms are contradictory).
0.56/0.75	EOF