%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SYN247-1 : TPTP v8.1.2. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof

% Computer : n031.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep  1 03:33:45 EDT 2023

% Result   : Unsatisfiable 11.40s 2.21s
% Output   : Proof 11.40s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN247-1 : TPTP v8.1.2. Released v1.1.0.
% 0.07/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34  % Computer : n031.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sat Aug 26 20:15:53 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 11.40/2.21  Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 11.40/2.21  
% 11.40/2.21  % SZS status Unsatisfiable
% 11.40/2.21  
% 11.40/2.21  % SZS output start Proof
% 11.40/2.21  Take the following subset of the input axioms:
% 11.40/2.21    fof(axiom_1, axiom, s0(d)).
% 11.40/2.21    fof(prove_this, negated_conjecture, ![X, Y]: ~m1(d, X, Y)).
% 11.40/2.21    fof(rule_032, axiom, ![F]: (m1(F, F, F) | ~s0(F))).
% 11.40/2.21  
% 11.40/2.21  Now clausify the problem and encode Horn clauses using encoding 3 of
% 11.40/2.21  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 11.40/2.21  We repeatedly replace C & s=t => u=v by the two clauses:
% 11.40/2.21    fresh(y, y, x1...xn) = u
% 11.40/2.21    C => fresh(s, t, x1...xn) = v
% 11.40/2.21  where fresh is a fresh function symbol and x1..xn are the free
% 11.40/2.21  variables of u and v.
% 11.40/2.21  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 11.40/2.21  input problem has no model of domain size 1).
% 11.40/2.21  
% 11.40/2.21  The encoding turns the above axioms into the following unit equations and goals:
% 11.40/2.21  
% 11.40/2.21  Axiom 1 (axiom_1): s0(d) = true2.
% 11.40/2.21  Axiom 2 (rule_032): fresh400(X, X, Y) = true2.
% 11.40/2.21  Axiom 3 (rule_032): fresh400(s0(X), true2, X) = m1(X, X, X).
% 11.40/2.21  
% 11.40/2.21  Goal 1 (prove_this): m1(d, X, Y) = true2.
% 11.40/2.21  The goal is true when:
% 11.40/2.21    X = d
% 11.40/2.21    Y = d
% 11.40/2.21  
% 11.40/2.21  Proof:
% 11.40/2.21    m1(d, d, d)
% 11.40/2.21  = { by axiom 3 (rule_032) R->L }
% 11.40/2.21    fresh400(s0(d), true2, d)
% 11.40/2.21  = { by axiom 1 (axiom_1) }
% 11.40/2.21    fresh400(true2, true2, d)
% 11.40/2.21  = { by axiom 2 (rule_032) }
% 11.40/2.21    true2
% 11.40/2.21  % SZS output end Proof
% 11.40/2.21  
% 11.40/2.21  RESULT: Unsatisfiable (the axioms are contradictory).
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