%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN214-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 : Thu Sep 24 03:15:29 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.59s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 23
% Syntax : Number of formulae : 101 ( 101 unt; 0 def)
% Number of atoms : 101 ( 100 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 5 con; 0-4 aty)
% Number of variables : 164 ( 164 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
s0(d) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] : p0(b,X) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X] : q0(X,d) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,Y] : m0(X,d,Y) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
l0(a) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [A,J] : ifeq(m0(A,A,J),true,m1(J,J,J),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f122,axiom,
! [C,B] : ifeq(p0(C,B),true,p1(B,B,B),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f147,axiom,
! [C,D,B] : ifeq(m0(C,D,B),true,q1(B,B,B),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f161,axiom,
! [E,D] : ifeq(q1(d,E,d),true,ifeq(q0(D,E),true,ifeq(s0(d),true,r1(D),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f162,axiom,
! [I] : ifeq(p0(I,I),true,s1(I),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f163,axiom,
! [H,F,G] : ifeq(s1(H),true,ifeq(q0(F,G),true,s1(F),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f169,axiom,
! [B,A,C,J] : ifeq(s1(B),true,ifeq(p0(A,A),true,ifeq(m0(C,B,J),true,l2(J,J),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f173,axiom,
! [B,C,A] : ifeq(p1(B,C,A),true,n2(A),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f186,axiom,
! [G,F] : ifeq(m1(G,G,F),true,p2(F,F,F),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f224,axiom,
! [G] : ifeq(r1(G),true,ifeq(l0(G),true,r2(G),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f274,axiom,
! [E,F,D] : ifeq(p2(E,F,D),true,n3(D),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f278,axiom,
! [H] : ifeq(n2(H),true,p3(H,H,H),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f292,axiom,
! [I,A,J] : ifeq(r2(I),true,ifeq(l2(A,A),true,ifeq(s1(J),true,q3(I,I),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f310,axiom,
! [A,B,J] : ifeq(p3(A,B,J),true,l4(J),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f330,axiom,
! [H,I,G,J] : ifeq(q3(H,I),true,ifeq(n3(G),true,ifeq(p0(J,G),true,r4(G),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f361,axiom,
! [I,H] : ifeq(r4(I),true,ifeq(l4(H),true,s5(H),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f363,negated_conjecture,
s5(c) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f364,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f365,plain,
s0(d) = true,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f378,plain,
! [X0] : p0(b,X0) = true,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f381,plain,
! [X0] : q0(X0,d) = true,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f383,plain,
! [X0,X1] : m0(X0,d,X1) = true,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f384,plain,
l0(a) = true,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f408,plain,
! [X0,X1] : ifeq(m0(X0,X0,X1),true,m1(X1,X1,X1),true) = true,
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f485,plain,
! [X0,X1] : ifeq(p0(X0,X1),true,p1(X1,X1,X1),true) = true,
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f510,plain,
! [X0,X1,X2] : ifeq(m0(X0,X1,X2),true,q1(X2,X2,X2),true) = true,
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f524,plain,
! [X0,X1] : ifeq(q1(d,X0,d),true,ifeq(q0(X1,X0),true,ifeq(s0(d),true,r1(X1),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f525,plain,
! [X0] : ifeq(p0(X0,X0),true,s1(X0),true) = true,
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f526,plain,
! [X0,X1,X2] : ifeq(s1(X0),true,ifeq(q0(X1,X2),true,s1(X1),true),true) = true,
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f532,plain,
! [X0,X1,X2,X3] : ifeq(s1(X0),true,ifeq(p0(X1,X1),true,ifeq(m0(X2,X0,X3),true,l2(X3,X3),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f169]) ).
fof(f536,plain,
! [X0,X1,X2] : ifeq(p1(X0,X1,X2),true,n2(X2),true) = true,
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f549,plain,
! [X0,X1] : ifeq(m1(X0,X0,X1),true,p2(X1,X1,X1),true) = true,
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f587,plain,
! [X0] : ifeq(r1(X0),true,ifeq(l0(X0),true,r2(X0),true),true) = true,
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f637,plain,
! [X0,X1,X2] : ifeq(p2(X0,X1,X2),true,n3(X2),true) = true,
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f641,plain,
! [X0] : ifeq(n2(X0),true,p3(X0,X0,X0),true) = true,
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f655,plain,
! [X0,X1,X2] : ifeq(r2(X0),true,ifeq(l2(X1,X1),true,ifeq(s1(X2),true,q3(X0,X0),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f292]) ).
fof(f673,plain,
! [X0,X1,X2] : ifeq(p3(X0,X1,X2),true,l4(X2),true) = true,
inference(cnf_transformation,[status(thm)],[f310]) ).
fof(f693,plain,
! [X0,X1,X2,X3] : ifeq(q3(X0,X1),true,ifeq(n3(X2),true,ifeq(p0(X3,X2),true,r4(X2),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f330]) ).
fof(f724,plain,
! [X0,X1] : ifeq(r4(X0),true,ifeq(l4(X1),true,s5(X1),true),true) = true,
inference(cnf_transformation,[status(thm)],[f361]) ).
fof(f726,plain,
s5(c) != true,
inference(cnf_transformation,[status(thm)],[f363]) ).
fof(f831,plain,
! [X0] : true = ifeq(true,true,m1(X0,X0,X0),true),
inference(paramodulation,[status(thm)],[f383,f408]) ).
fof(f835,plain,
! [X0] : true = m1(X0,X0,X0),
inference(forward_demodulation,[status(thm)],[f364,f831]) ).
fof(f933,plain,
true = ifeq(true,true,s1(b),true),
inference(paramodulation,[status(thm)],[f378,f525]) ).
fof(f934,plain,
true = s1(b),
inference(forward_demodulation,[status(thm)],[f364,f933]) ).
fof(f2914,plain,
! [X0] : true = ifeq(true,true,p1(X0,X0,X0),true),
inference(paramodulation,[status(thm)],[f378,f485]) ).
fof(f2922,plain,
! [X0] : true = p1(X0,X0,X0),
inference(forward_demodulation,[status(thm)],[f364,f2914]) ).
fof(f2951,plain,
! [X0] : true = ifeq(true,true,n2(X0),true),
inference(paramodulation,[status(thm)],[f2922,f536]) ).
fof(f2964,plain,
! [X0] : true = n2(X0),
inference(forward_demodulation,[status(thm)],[f364,f2951]) ).
fof(f2965,plain,
! [X0] : ifeq(true,true,p3(X0,X0,X0),true) = true,
inference(backward_demodulation,[status(thm)],[f2964,f641]) ).
fof(f2969,plain,
! [X0] : p3(X0,X0,X0) = true,
inference(forward_demodulation,[status(thm)],[f364,f2965]) ).
fof(f2977,plain,
! [X0] : true = ifeq(true,true,l4(X0),true),
inference(paramodulation,[status(thm)],[f2969,f673]) ).
fof(f2978,plain,
! [X0] : true = l4(X0),
inference(forward_demodulation,[status(thm)],[f364,f2977]) ).
fof(f2981,plain,
! [X0,X1] : ifeq(r4(X0),true,ifeq(true,true,s5(X1),true),true) = true,
inference(backward_demodulation,[status(thm)],[f2978,f724]) ).
fof(f2983,plain,
! [X0,X1] : ifeq(r4(X0),true,s5(X1),true) = true,
inference(forward_demodulation,[status(thm)],[f364,f2981]) ).
fof(f3646,plain,
! [X0] : true = ifeq(true,true,q1(X0,X0,X0),true),
inference(paramodulation,[status(thm)],[f383,f510]) ).
fof(f3660,plain,
! [X0] : true = q1(X0,X0,X0),
inference(forward_demodulation,[status(thm)],[f364,f3646]) ).
fof(f3761,plain,
! [X0,X1] : ifeq(q1(d,X0,d),true,ifeq(q0(X1,X0),true,ifeq(true,true,r1(X1),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f365,f524]) ).
fof(f3762,plain,
! [X0,X1] : ifeq(q1(d,X0,d),true,ifeq(q0(X1,X0),true,r1(X1),true),true) = true,
inference(forward_demodulation,[status(thm)],[f364,f3761]) ).
fof(f3763,plain,
! [X0] : true = ifeq(true,true,ifeq(q0(X0,d),true,r1(X0),true),true),
inference(paramodulation,[status(thm)],[f3660,f3762]) ).
fof(f3770,plain,
! [X0] : true = ifeq(q0(X0,d),true,r1(X0),true),
inference(forward_demodulation,[status(thm)],[f364,f3763]) ).
fof(f3771,plain,
! [X0] : true = ifeq(true,true,r1(X0),true),
inference(forward_demodulation,[status(thm)],[f381,f3770]) ).
fof(f3772,plain,
! [X0] : true = r1(X0),
inference(forward_demodulation,[status(thm)],[f364,f3771]) ).
fof(f3798,plain,
! [X0,X1] : true = ifeq(s1(X0),true,ifeq(true,true,s1(X1),true),true),
inference(paramodulation,[status(thm)],[f381,f526]) ).
fof(f3808,plain,
! [X0,X1] : true = ifeq(s1(X0),true,s1(X1),true),
inference(forward_demodulation,[status(thm)],[f364,f3798]) ).
fof(f3831,plain,
! [X0] : true = ifeq(true,true,s1(X0),true),
inference(paramodulation,[status(thm)],[f934,f3808]) ).
fof(f3833,plain,
! [X0] : true = s1(X0),
inference(forward_demodulation,[status(thm)],[f364,f3831]) ).
fof(f3905,plain,
! [X1,X2,X0,X3] : ifeq(true,true,ifeq(p0(X1,X1),true,ifeq(m0(X2,X0,X3),true,l2(X3,X3),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f3833,f532]) ).
fof(f3906,plain,
! [X0,X1,X2,X3] : ifeq(p0(X0,X0),true,ifeq(m0(X1,X2,X3),true,l2(X3,X3),true),true) = true,
inference(forward_demodulation,[status(thm)],[f364,f3905]) ).
fof(f3915,plain,
! [X0,X1] : true = ifeq(p0(X0,X0),true,ifeq(true,true,l2(X1,X1),true),true),
inference(paramodulation,[status(thm)],[f383,f3906]) ).
fof(f3924,plain,
! [X0,X1] : true = ifeq(p0(X0,X0),true,l2(X1,X1),true),
inference(forward_demodulation,[status(thm)],[f364,f3915]) ).
fof(f4242,plain,
! [X0] : true = ifeq(true,true,p2(X0,X0,X0),true),
inference(paramodulation,[status(thm)],[f835,f549]) ).
fof(f4251,plain,
! [X0] : true = p2(X0,X0,X0),
inference(forward_demodulation,[status(thm)],[f364,f4242]) ).
fof(f4264,plain,
! [X0] : true = ifeq(true,true,n3(X0),true),
inference(paramodulation,[status(thm)],[f4251,f637]) ).
fof(f4275,plain,
! [X0] : true = n3(X0),
inference(forward_demodulation,[status(thm)],[f364,f4264]) ).
fof(f4896,plain,
! [X0] : true = ifeq(true,true,l2(X0,X0),true),
inference(paramodulation,[status(thm)],[f378,f3924]) ).
fof(f4897,plain,
! [X0] : true = l2(X0,X0),
inference(forward_demodulation,[status(thm)],[f364,f4896]) ).
fof(f4957,plain,
! [X0] : ifeq(true,true,ifeq(l0(X0),true,r2(X0),true),true) = true,
inference(forward_demodulation,[status(thm)],[f3772,f587]) ).
fof(f4958,plain,
! [X0] : ifeq(l0(X0),true,r2(X0),true) = true,
inference(forward_demodulation,[status(thm)],[f364,f4957]) ).
fof(f4960,plain,
true = ifeq(true,true,r2(a),true),
inference(paramodulation,[status(thm)],[f384,f4958]) ).
fof(f4962,plain,
true = r2(a),
inference(forward_demodulation,[status(thm)],[f364,f4960]) ).
fof(f6456,plain,
! [X0,X2] : ifeq(r2(X0),true,ifeq(true,true,ifeq(s1(X2),true,q3(X0,X0),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f4897,f655]) ).
fof(f6457,plain,
! [X0,X2] : ifeq(r2(X0),true,ifeq(s1(X2),true,q3(X0,X0),true),true) = true,
inference(forward_demodulation,[status(thm)],[f364,f6456]) ).
fof(f6458,plain,
! [X0] : ifeq(r2(X0),true,ifeq(true,true,q3(X0,X0),true),true) = true,
inference(forward_demodulation,[status(thm)],[f3833,f6457]) ).
fof(f6459,plain,
! [X0] : ifeq(r2(X0),true,q3(X0,X0),true) = true,
inference(forward_demodulation,[status(thm)],[f364,f6458]) ).
fof(f6460,plain,
true = ifeq(true,true,q3(a,a),true),
inference(paramodulation,[status(thm)],[f4962,f6459]) ).
fof(f6462,plain,
true = q3(a,a),
inference(forward_demodulation,[status(thm)],[f364,f6460]) ).
fof(f7426,plain,
! [X0,X1,X3,X2] : ifeq(q3(X0,X1),true,ifeq(true,true,ifeq(p0(X3,X2),true,r4(X2),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f4275,f693]) ).
fof(f7427,plain,
! [X0,X1,X2,X3] : ifeq(q3(X0,X1),true,ifeq(p0(X2,X3),true,r4(X3),true),true) = true,
inference(forward_demodulation,[status(thm)],[f364,f7426]) ).
fof(f7428,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(p0(X0,X1),true,r4(X1),true),true),
inference(paramodulation,[status(thm)],[f6462,f7427]) ).
fof(f7435,plain,
! [X0,X1] : true = ifeq(p0(X0,X1),true,r4(X1),true),
inference(forward_demodulation,[status(thm)],[f364,f7428]) ).
fof(f7814,plain,
! [X0] : true = ifeq(true,true,r4(X0),true),
inference(paramodulation,[status(thm)],[f378,f7435]) ).
fof(f7816,plain,
! [X0] : true = r4(X0),
inference(forward_demodulation,[status(thm)],[f364,f7814]) ).
fof(f7819,plain,
! [X0] : ifeq(true,true,s5(X0),true) = true,
inference(backward_demodulation,[status(thm)],[f7816,f2983]) ).
fof(f7820,plain,
! [X0] : s5(X0) = true,
inference(forward_demodulation,[status(thm)],[f364,f7819]) ).
fof(f7821,plain,
$false,
inference(resolution,[status(thm)],[f7820,f726]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN214-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 10:46:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.40 % Drodi V4.1.1
% 0.14/0.59 % Refutation found
% 0.14/0.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.40/0.62 % Elapsed time: 0.245612 seconds
% 0.40/0.62 % CPU time: 1.597302 seconds
% 0.40/0.62 % Total memory used: 77.015 MB
% 0.40/0.62 % Net memory used: 75.543 MB
%------------------------------------------------------------------------------